Since your post probably came from reading BrowserUk's question about Bidirectional lookup algorithm, let's put your theory to the test with the method he used:

use Devel::Size qw/total_size/;

$h{$_} = 1 for "aaaaa".."zzzzz";
$elements_size += total_size $_ for %h;
$hash_size = total_size \%h;
print <<INFO;
Total size of the contained elements: $elements_size
Total size of the hash:               $hash_size
INFO
__DATA__
Total size of the contained elements: 1223781728
Total size of the hash:               1167897536
[download]

It sure looks like I did something wrong. But since keys are constant strings (of fixed size), they probably take less space than a string in a scalar (scalar have all sorts of additional information, and a bit of extra space to avoid constant reallocation), so in the end I don't think I made any mistakes here. And I'm saying "probably" because I didn't check in the guts.

A lot of data in a hash sure takes a lot of memory, same goes for arrays because a lot of data will take a lot of memory unless it's properties allow for a very effective compression. If you only use pure perl, trying to avoid a hash because they are "bad" has very high probability of just being worse (hashes are an excellent compromise between algorythm complexity and memory consumption).