CaptainSalad2 - Basically.. yes. The current setup could appear to Google that you're hiding bad backlinks via 301s. That was an old spammer's trick... and even before Penguin, depending on the level of transgression, it would cause problems in Google. With Penguin, I'm sure the bar has been raised. You can't escape bad backlinks using 301s.
Assuming that these redirected bad backlinks were your only issue, removing the 301 would remove the algorithmic aspects of the "penalty" from the clean domain.
That doesn't mean that the clean domain would automatically bounce up to pre-Penguin levels. As your post suggests, five backlinks to the clean domain isn't very much, and they might not be sufficient for the clean domain to rank. You might need to build up your content and promote it to create a good enough backlink profile to build up your rankings. I would avoid any types of linkbuilding that are going to look artificial, as I'm sure that the domain has been flagged. You didn't mention whether there was any manual penalty.
Note, btw, that I changed the original title you'd posted, "301 penalty drop away once 301 removed?", to the current title, "Remove 301 from spammy alias domain to help Penguin recovery?" for clarity, or as much clarity as I could get into less than 70 characters.