D'oh! The point of undef is that it evaluates to false in logic statements (see the compound statement section of perlsyn). So you don't need to explicitely test against it:

my $user = get_userid();
print "UNDEF" unless $user;
print "<p>whoa whoa whao $user" if $user;
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(oh, you don't need to bracket the conditions, when they're modifiers, and unless is the equivalent of "if not")