Note that for a command line script/app expected behavior is that the app/script exits after dumping help given --help on the command line. Maybe you would be better to use something like --hints instead where you want to dump the help and continue?

You already answered your own question by following up to state that -exitval => 'NOEXIT' works. I had found this to work just fine, as well. But it wouldn't be Perl if it didn't arouse curiosity. I was curious if I could override CORE::GLOBAL::exit effectively. Turns out I can (though this isn't to say I should):

#!/usr/bin/env perl

use strict;
use warnings;

our $override_exit = 0;
BEGIN {
    no warnings 'redefine';
    *CORE::GLOBAL::exit = sub :prototype(;$) {
        if ($override_exit) {
            warn "EXIT_OVERRIDE\n";
        }
        else {
            CORE::exit($_[0] // 0);
        }
    };
}

use Pod::Usage;

{
    local $override_exit = 1;

    print "Calling pod2usage(1)\n";
    pod2usage(1);
    print "We are still here after overriding exit.\n";
}

print "calling pod2usage with -exitval => 'NOEXIT'\n";
pod2usage(-exitval => 'NOEXIT');
print "We are still here after using -exitval => 'NOEXIT'.\n";
[download]

This produces the following output:

Calling pod2usage(1)
EXIT_OVERRIDE
We are still here after overriding exit.
calling pod2usage with -exitval => 'NOEXIT'
We are still here after using -exitval => 'NOEXIT'.
[download]

So this demonstrates that NOEXIT works, and that overriding CORE::GLOBAL::exit can work.

system(qq{perldoc $0});

Sorry, but no. I have much respect for TIMTOWTDI, but given that Pod::Usage has been in the Perl core for over 20 years and the question was already solved in the OP, then a solution that calls an external program that may not be installed, is brittle in other ways (PATH and $0), doesn't do the same thing as the OP is asking, and introduces a potential security vulnerability ($0 can be assigned to), is the Wrong Way.

Explain to me your objection. Pod::Usage seems to rely on underlying "formatters", including perldoc. Does your object rely simply on the hypothetical that $0 can be reassigned or that there exist linux distros that include perl but not perldoc by default, like Debian?