It depends on whether your new sill cock has a pipe thread on the end or is sweat.
If it's sweat, I would cut the pipe to the right of the subject matter in that photo and solder a 1/2 inch ball valve in between the supply pipe and the sill cock. The ball valve would allow you to shut the water off to the sill cock to replace the washer in it (or whatever other servicing needs to be done to the sillcock).
Don't believe anyone who tells you to take a ball valve apart before soldering it into place... you're way more likely to have a leak in the ball valve by taking it apart prior to soldering it than heating it up to solder it in place. As long as the ball valve is OPEN when you solder it, you should have no problems. (Personally, I like to remove the handle from ball valves before soldering them just to prevent my burning the plastic on the handle with the torch.
The trick is to make sure the ball valve is open when you solder it, and ensure that the air inside the piping has a path by which it can expand other than through the joint you're trying to solder. So, in your case both the ball valve and the sillcock should be wide open when you're soldering. Also, don't close either the ball valve or the sillcock until they've cooled down to near ambient temperatures.
No, you don't have to solder to install a new sillcock, but that's the most reliable way of making a plumbing connection that I know of.