Hmmm.

AFAIK as long as you make sure you close STDOUT and STDIN (or at least not use them ever) you should be fine, but the webserver may decide the request is taking too long and terminate it anyway. You can probably fork() a separate process to get around that (make sure you close STDIN and STDOUT before the fork or in the child process, though!)

update:

# process input
# print HTML page

close STDIN;
close STDOUT;
my $child_pid = fork();
if (!defined $child_pid) {
  die "Can't fork child process";
}
if ($child_pid) {
  # in parent process
  exit;
}
# do long processing here.
[download]

You might need to set some signal handlers and/or close additional filehandles you've opened in the parent process, but as a general outline, this should work.