Theoretically, no. But in 2006, I had problems with some software at one site with a Debian installation. Then there are things like running Firefox, where some plugins only existed in 32-bit form. (Adobe Flash for one, but that was eventually fixed.)

To run 32-bit programs on Linux, the ld linker must correctly search for the right 32-bit libraries at run-time. This can be accomplished with chroot environments, or with a more sophisticated ld.

This might be old news. By now (2008) such kinks have probably been worked out.