Yes and no.

Yes. You get rid of zombies on some systems, but you should rather use

use POSIX ":sys_wait_h";

$SIG{CHLD} = sub {
    my $kid;
    do {
        $kid = waitpid(-1,&WNOHANG);
    } until $kid == -1;
}
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This will collect all the zombies immediatly as they become 'undead'.

No. This will not solve the problem of missing close. When open(FH,'...|') is called, pipe is created as a pair of file descriptors. These fil desrciptors will not be reused until explicitly closed by close syscall. Therefore if your program will serve thousands of requests in one process you will run out of file descriptors. One possible solution to this is to specify MaxRequestsPerChild 200 Apache configuration directive to limit one server process to serve only 200 requests before it dies. But the whole idea of long-running mod_perl precesses is somehow hindered by this.