I currently have a 39 gallon tank with 5 platies, 6 danios, 4 cories, and 8 black neons. Would it be pushing it to buy 1 or 2 groups of hatchetfish? Also, I heard somewhere that they can be a bit aggressive. Is this true or am I confused with some other fish?
No one here is going to council you to add fish of any kind to a tank that is already overcrowded. We have an obligation to help people develop a healthy understanding of tank care, which includes not over crowding.
The rule of thumb is 1" of adult fish size per gallon of tank. Research the fish you want....if they say they should be kept in a school of 6, then we are not going to say you can get 2 of them....
Normally, I would say that shrimp don't add too much bioload, but that's in a tank that isn't already overloaded. They do have a bioload, just not much of one. There will be a straw that will break the camel's back, and like Susitna said, I just can't counsel someone to add anything to an overstocked tank.
Aside from this, shrimp are pretty sensitive to nitrates, and will likely not survive for long in this tank, thus further polluting the water.