Does Perl even support a hash 4 levels deep? What is the limit on that anyway?

Since multilevel hashes are really just hashes holding references to other (anonymous) hashes, I don't think there is any real limit. Try e.g. the following:

#!/usr/bin/perl

use strict;
use warnings;
use feature qw/say/;

use Data::Dumper;

my %hash = ();
my $hashref = \%hash;

for(1..255) {
    $hashref = $hashref->{$_} = {};
}

print Dumper \%hash;
[download]

This works like a charm and as expected.

Bisecting this, I found I can go up to 4028 layers of indirection before Perl segfaults at 4029. (And 4028 produces 178 MiB of output from Data::Dumper.)