A lot depends on the board, of course, but IIRC, the power supply in an ATX
box has more clearance for the board to slip under. It's those connectors
that will probably give you fits. The mounting holes should be very
close--if it's not a perfect match, you can always use some extra nylon PC
board standoffs at critical points.
It may be more trouble than it's worth. ATX has been out for so many
years that I'd probably just look around for a recycled PC with the case I
wanted.
Cheers,
Chuck