With the standard CGI model, where your web server forks off a process to run an external program, it's possible to do such a thing, but it seems really tricky and fragile.
It's not really that tricky or fragile so long as the external program knows it's going to run a perl program. That's how CGI::SpeedyCGI (a.k.a PersistentPerl) does it. It has a small binary front-end that looks for the persistent perl process, starts it if it doesn't exist already, and then hands off control to it. All you have to do is change your shebang line to point at that front-end. (And code for its persistent environment.)
-sauoq "My two cents aren't worth a dime.";
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