Have a dumb questions.. But why not make patterns out of foam and just paint the foam? That blue foam stuff for isolating concrete floors should standup to the ramming of the sand i figure. And its cheap, light weight and can be formed with a nailfile if out of wood tools.
I've wondered that a time or two, but actually find wood easier to work and finish. I think the problem with foam isn't necessarily that it would crush, but that it would move/compress/expand under ramming pressure and the sand is probably not going to like that. Also it might be ticklish to extract the pattern -- what do you screw into?
Finish would need to be a lot more extensive than just paint. There are some proprietary hard sufacers -- used for stage props, I believe, but you get into money there, plus lots of finish work.
Theory and thought experiments must always take back seat to reality., though,and I haven't tried it. So can't really say yes or no to it. Unless hard surfaced, I imagine it wouldn't last long, though.
Of course there's lost foam casting, which is altogether different. I've done that with aluminum, and believe I wrote something about it somewhere on this forum a while back.
