Yes, post_accept and process_request are executed by the same process. Here's the sample that demonstrates this:

use strict;
use warnings;

MyServer->run(port => 7777);

package MyServer;

use base qw(Net::Server::PreFork);

sub post_accept {
    warn "post accept in $$\n";
}

sub process_request {
    warn "process request in $$\n";
}

__END__
...
post accept in 9238
process request in 9238
post accept in 9241
process request in 9241
post accept in 9242
process request in 9242
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