The only draw back I see, if you put Styrofoam on the floor and then cover it directly with vinyl, and then you walk on it, over time, the Styrofoam will get squashed and you many end up with a bunch of dimples or footprint depressions in the Styrofoam.
I have an access port under the shower in my Outback. I can see how the floor is put together where it's been cut out for the plumbing that comes through the floor.
There is a layer of 1 inch thick Styrofoam, on top of that, there is a 1/4 inch sheet of plywood, on top of that is the vinyl.
About insulation value, yes it will help and it will make the floor warmer in the winter, but it will also make it feel squishy under your feet.
It's really 6 of one / half-a-dozen of another. I don't think 1/4 inch Styrofoam will hurt anything, just not sure how it will hold up under the weight of a someone's foot.