Negative. Using or requiring APR first (use APR; use APR::UUID;) does not fix the problem. Not using APR at all isn't a problem here, since the command line version at the end of my post works.
Second, it works as-is on every platform except for OpenBSD. I think that's the marker of something strange going on here.
In fact, just 'use APR;' in the Makefile.PL above causes the same problem.
Update: I just got a copy of the mp2.0.2 source on the server in question. the uuid tests pass fine:
test:~/mod_perl-2.0.2/t$ perl -T -Ilib apr-ext/uuid.t
# Running under perl version 5.008006 for openbsd
# Current time local: Sat Dec 3 19:12:38 2005
# Current time GMT: Sat Dec 3 19:12:38 2005
# Using Test.pm version 1.25
# Using Apache/Test.pm version 1.27