I don't use mod_perl (and don't know much about it, but which one are you using?) but suspect you can trap the errors using eval; that's a supposition supported by this:

https://perl.apache.org/docs/2.0/user/porting/compat.html

"In mod_perl 2.0, <Perl> sections errors are now always fatal. Any error in them will cause an immediate server startup abort, dumping the error to STDERR. To avoid this, eval {} can be used to trap errors and ignore them. In mod_perl 1.0, strict was somewhat of a misnomer." (direct from big-G)

FWIW, trapping with an eval does NOT appear to be exclusively mod_perl 2; SO has this; unsurprisingly, so does PM.