You do not provide enough context for anyone to provide meaningful advice. The best we can do is answer with vague generalities.

Ideally you should have regression tests for your programs that you can use to verify that they run correctly under the newer OS.

In my experience, perl programs written under older versions of Perl work fine under newer versions. The risks may lie in programs that depend on modules that have undergone changes that are not backward compatible. There are also risks involving progams depend on the operating environment. There are risks that modules you depend on that were bundled with RHEL3 are not bundled with RHEL7. Core perl modules will probably be fine.

Given that you haven't given any indication of what kinds of programs you have, or what modules they depend on, it is impossible to give an answer to your question. All that you tell us is that you have a big ball of programs.

In my experience, well written progams have the fewest problems with changes in operating environment. Badly written programs can break under the slightest changes. Badly maintained programs are also vulnerable.

If you don't know anything about the programs, the answer to your question is "maybe". Good luck.