(They're called "Tapcon" screws, not con-tap screws.)
If I wanted to install a floor over a concrete slab, I'd be more inclined to glue down a product called Delta FL, screw 1/2 inch plywood down to the Delta FL, and then install whatever flooring I want over the plywood. Delta FL is basically a sturdy plastic material that comes in a roll about 4 feet wide. It has lots of "cones" molded into it that act like little feet holding it an inch or so above the concrete slab. Those sturdy little feet are plenty strong enough collectively to support a floor. Since it's made of plastic, it's also a vapour barrier and since it traps air between the concrete slab and the wood subfloor above, it effectively provides a good degree of insulation from the cold concrete.
I'm not familiar with using the blue or pink foam on floors, but I can tell you a little bit about them which probably will answer your question so you'll understand why you DO NOT need to use a vapour barrier with either the blue or pink foam.
Polystyrene foam comes in two kinds, expanded and extruded. The expanded polystyrene foam is the white stuff you see that seems to be made of "beads". The blue or pink foam is EXTRUDED polystyrene. One of the differences between the two is that expanded polystyrene is made using much more blowing gas than extruded polystyrene, so that the gas bubbles formed when expanded polystyrene is made are often large enough so that they allow interconnection of the bubbles in the foam. That allows air and moisture to move between the bubbles, and potentially right through the expanded polystyrene foam. Extruded polystyrene uses much less blowing gas in it's manufacture, and so the bubbles inside extruded polystyrene foam are much smaller and don't interconnect. The result is that air and moisture can't move through extruded polystyrene foam like they can through the interconnected bubbles in expanded polystyrene foam, and so extruded polystyrene foam is impermeable to both air and moisture and therefore doesn't need a vapour barrier. Extruded polystyrene doesn't need a separate vapour barrier because it's impermeable to air, water and humidity. You don't need a sheet of plastic to keep moist air out of it because moist air can't get into it in the first place.
I think that using Delta FL would do the same thing for you as using wood strips on the floor with extruded polystyrene foam insulation between the strips. Also, I can't help thinking that using any wood on a slab on grade is a bad idea because if any moisture does come up through the slab, what's to prevent that wood from rotting? Delta FL is plastic, and won't rot. You glue it down.
Also, I'd be very reluctant to use a ceramic tile in your laundry room. If your washer gets out of balance and it starts dancing around your laundry room, I could see that it might start cracking your ceramic tiles for you. Also, ceramic tile floors are relatively smooth and potentially slippery when wet. I'd say that a much better choice of flooring for a laundry room would be synthetic rubber floor tiles, which are what's used in gyms under weight lifting equipment. Synthetic rubber flooring is also used in a wide variety of commercial settings where you want an extremely durable floor that offers the wide variety of colours and styles that normally are only available in residential floorings, like sheet vinyl and real linoleums.
Also, the coefficient of friction between the rubber soles of your sneakers and synthetic rubber flooring is very high, so you'll have good traction even with an occasionally wet laundry room floor. But, rubber flooring is most commonly used in commercial settings, and you can get rubber flooring for entrance ways that has an embossed surface for even better traction under wet conditions. I installed synthetic rubber stair treads in both the front and back stair wells in my apartment block partly because I knew that they would provide excellent traction for rubber soled shoes. So, if anyone ever slips and falls in my front or back stair wells, it would be hard to suggest that the steps were slippery. The judge would be convinced that the person would have fallen regardless of what kind of treads I had on those steps. And I like the feeling of knowing that I'M protected from the nuts out there that would sue me for injuring themselves as a result of their own carelessness.
Probably the biggest name in synthetic rubber flooring is Johnsonite, and I'd spend an evening at Johnsonite > Home
to see the various kinds, colours, sizes and styles of synthetic rubber floor tiles available from Johnsonite. I think you'll agree that synthetic rubber floor tiles would be a simpler and more practical flooring for your laundry room than ceramic tiling.
Synthetic rubber floor tiles are NOT inexpensive. They're a relatively expensive floor, but they're also a near indestructable floor, and in my view, a much better flooring material for a 200 pound unbalanced washing machine with 300 pounds of water in it to be dancing on.