Yep, and I do it all the time.
But, please don't tell me that you have mosaic tiles in your shower that are 1 inch square or something terrible like that. It'd probably be easier to cover up those walls with a tub surround that to clean all the grout.
Basically, mildew feeds on soap or soap scum wherever it can get a good grip on the surface it's on so it won't be washed away by the shower spray.
The first thing to do is buy some phosphoric acid based toilet bowl cleaner in any janitorial supply store or the cleaning aisle of your local home center. The toilet bowl cleaner will be gelled so that it sticks to vertical surface. You want to stay away from any toilet bowl cleaner that contains hydrochloric acid cuz it'll attach any crome plating, and you don't want a phosphoric acid content any higher than 20 percent max. cuz you migh dissolve too much of the grout.
Now, use masking tape and tape off the entire area you want to clean into areas of about 2 feet by 3 feet, or about 6 square feet each. Starting at the bottom of the tiling, use a spoon, stick or paint brush to get bathroom cleaner onto your tiling and use a rubber squeegee to remove it to the grout lines (so that it's only in the grout lines) in those 6 square feet you're working on at the time.
Now, take a denture cleaning brush or a small nylon brush (that kinda looks like a toothbrush) and scrub the acid while fairly regularily wiping the toilet bowl cleaner back into the grout lines with the squeegee.
PS: If you can, wear latex gloves while doing this because the acid can start annoying your skin after a while. Also, try to get either a cheap rubber squeegee from your local pharmacy for removing the water from bathroom ceramic tiles and shower doors, or go to a janitorial supply store and pay more to get a professional window cleaner's squeegee (that will have replaceable rubber wipers). The best names in squeegees are Ettore and Mallory. You can get both in brass, but the phosphoric acid might stain the brass a bit. If you want to keep the squeegee looking good for regular use, get a stainless steel one.
Anyhow, the purpose of the acid is not to clean the mildew, but to open up the porous surface of the grout which is probably completely plugged with soap scum. Not only will the acid dissolve the soap scum, it'll dissolve the top hundredth of an inch or so of the grout, where it's not all clogged with soap scum anymore.
Once you've removed a lot of the mildew and you can see that the acid is dissolving the grout a TINY bit, use a damp sponge to clean off the grout lines and rinse them off with clean water. You're finished using the acid now. Allow the tile to dry overnight.
After you do each section, use a razor scraper to cut the tape off between it an the next section so you don't leave the areas under the tape undone.
Now, use bleach straight out of the jug and your little brush to clean the grout lines with bleach. Instead of tape, just do the horizontal lines in order and the vertical lines in order and use a non-permanent felt pen to mark where you left off if the phone rings.
Time is on your side at this step. The bleach will penetrate deeper and deeper into the grout as long as the surface of the grout remains wet with bleach. So, you keep applying bleach to drive it as deep as necessary into the grout to remove all the mildew.
If you find that there's some stubborn spots that won't come clean, the surface of the grout may still be clogged with soap scum in those areas, so you might want to try giving just those areas another shot of acid to open up the surface porosity. If doing that doesn't help the bleach penetrate into the grout, you may have to remove that grout and regrout the grout line at that point. (So far with 21 bathrooms with ceramic tile over the tub/shower over 20 years, I haven't replaced more than about 4 feet of grout, and half of that was on a single job.
Anyhow, just keep applying bleach every few hours until the grout comes clean. Then, rinse the ceramic tiling off with clean water to wash off the bleach.
Now, give the ceramic tiling 2 days or so to dry, and apply a film forming acrylic grout sealer like this one:
Glaze N' Seal
The above is the best film forming acrylic sealer I know of.
Alternatively, let the bathroom dry for a few days more, and apply Tile Lab's "SurfaceGard" penetrating grout sealer.
If you find that the SurfaceGard doesn't seem to work well for you and water doesn't bead up on it afterward, you can try applying Tile Lab's "Gloss Sealer and Finish" or "Matte Sealer and Finish".
I like the Glaze 'N Seal sealer because it's a cross linking acrylic that forms a very hard and impermeable acrylic coating over the grout lines. This allows me to clean soap scum off of bathroom walls using phosphoric acid without the acid contacting the grout. That's because of the clear film of acrylic sealer over the grout lines.
I like Tile Lab "Gloss" and "Matte" sealers because they're the only acrylic grout sealers I know of that are actually easy to remove. The problem is that this product forms a film that's permeable enough to let humidity in the air through it. So, if someone goes and paints over their grout lines without cleaning them first, the result will be mildew growing in the grout UNDER the sealer. But, at least it's easy to remove the sealer from the mildewed spots, clean off the mildew, and re-seal.
Sealing grout is simple. If you can draw a more or less straight line, you can seal grout. Simply go to any art supply store and buy a "script" style paint brush, which when wet and held with light pressure against a piece of paper will give you a wet trace about the same width as your grout lines. Script paint brushes have longer bristles for less dipping and less dripping.
Hold a small container (I find a photographic film container works well) with some grout sealer in it AND a light (I find a 7 watt CFL works well) in one hand and paint the grout sealer on with the other. You want to be able to see the reflection of the light in the wet sealer to ensure you're covering the whole grout line.
I like to start at the top horizontal line and end up putting three coats on each line. Don't do the same line over and over again. You want the grout sealer to dry on each line before putting the next coat on.
The TV commercial showing someone actually painting grout sealer on the vertical lines was filmed by people who've never sealed grout. To seal the vertical lines, you just deposit a drop of grout sealer at the top of the grout line and just watch it as it goes down the grout line. If it slows down, add some more sealer to the grout line above the drop. If it gets away on you by running down the tile face, clean the sealer off the tile face and carry on. The first vertical coat will have the drop trying to get away the most often. By the time you get to the 3rd coat, you'll be doing 3 vertical lines at a time.
And, three coats of the Glaze 'N Seal will last you a good 10 years or better.
Post again if you want to know how to clean mildew staining off of silicone caulk.