I'm not 100% sure what type of foam you are talking about, but I have worked with quite a few different kinds of foam for prototyping. Most people think of the white packaging material when they think of Styrofoam and that would be pretty much useless for building anything that needs accuracy for strength. Large pink/blue foam sheets that are used for insulation are better, but still it is difficult to get a smooth finish on them and isn't very strong, I wouldn't recommend this either.
The type of foam I would recommend for this is a very dense yellow/green polyurethane foam. This foam is very dense and extremely strong as far as foams go. It can be cut and shaped with pretty much any wood working tools, files, sandpaper etc. I have even used dremels, power sanders, and I've seen it put on a lathe with great results. You can use most paints and finishes on it and get it looking very good, someone wouldn't even think its foam if you spent enough time surfacing it. The only drawbacks are that this stuff is not cheap at all, much more expensive then would, and it is very hazardous, wear a mask/respirator while working with it.
Not sure what type of foam your dad has, but if you had a picture I might be able to give some insight into how it would work.
Thus being said foam is really only good for prototyping. In this case of a desk I could see it being useful for making small scale mock ups maybe 1/10 size, but balsa would would probably be even better and cheaper. I can't really imagine a desk made primarily out of foam, the biggest issue I see would be with fasteners. Bolts and screws would just pull through the foam unless you had massive washer type things and it still wouldn't be very ideal. If you try to make it one huge solid piece with a lot of supports then your desk is gonna cost a fortune to ship even if it weighs 5lbs. When you go into best-buy and buy a desk the box its goosing to come in is probably less then 3 inches thick.
I don't see foam being a good solution.