Okay, I got this working with

#test.pl
use warnings;
use strict;
use DBM::Deep;
use Data::Dumper;
use LWP::UserAgent;
use Test::More qw(no_plan);

my $hash = DBM::Deep->new("foo.db");
my $user_agent = LWP::UserAgent->new;

$Data::Dumper::Terse=1;

my $user_agent_dumped = Dumper($user_agent);
$hash->{ua_1} = $user_agent_dumped;

my $user_agent_recreated = eval ( $hash->{ua_1} );

isa_ok($user_agent_recreated,'LWP::UserAgent'); #passes
[download]

Thanks to the monks who helped me with my followup at Getting back $object from eval(Dumper($object))