Lots of designs use extruded foam with cap strips for ribs. Yes, solvents will destroy them.
Continuous white bead foam will be a LOT heavier than separate extruded foam ribs. The white foam is very weak, so if you used it you'd need more ribs or just to make it solid. And if it's solid, on a typical ultralight, it will be heavy. Let's say you have 130 square feet, 28 foot span, 15 percent airfoil, and the foam takes up 80 percent of it. You're talking about maybe 58 lbs of white foam! 3/4 inch wide ribs with 1/8 inch cap strips (guessing) might be more like 0.4 lbs apiece. If you use them every 18 inches, that's 8 lbs. Built up ones are probably even lighter.