Not really. enqueue gets its ID from Minion::Backend::Pg::enqueue, which itself gets the ID by doing an SQL insert query that ends with RETURNING id, which means that the ID returned by enqueue is the ID of the row inserted into the database.
Instead, you could use a hash mapping the IDs returned by enqueue to the GUIDs generated by Data::UUID. Something like:
my $internal_id = $minion->enqueue(foo => [@args]);
my $external_id = Data::UUID->new->create_str;
$self->extern_to_intern_map{$external_id} = $internal_id;
(note that extern_to_intern_map will grow without ever shrinking; if your application is running for a long time, you may want to explicitly delete old mappings)