I'm studying history of Europe from the year 300-476 AD, so this is slightly out of my area, but I feel I can still get a decent answer out.

Essentially, yes and no- depending on which tribe you were a part of, weather it was a time of peace, and if the Romans had a sympathetic Emperor.

At that time, we do see migrations of Germanic peoples into Roman frontier provinces. Of course, you would be forced to disarm and hand over some sort of tribute, but odds are, with some effort you could emigrate.

So long as you have no issue paying taxes to the Romans and giving up certain parts of your Germanic lifestyle, there shouldn't be an issue. Of course, it also depends on the local governor and his attitude as well. But, in short, especially in a time where the Goths are looking to give the Romans a fight, you could definetely increase your odds by joining some Roman auxiliary forces- which gives you the added benefit of becoming a citizen after 25 years.

Hope this is at least slightly clarifying, feel free to comment below if I got anything wrong/anybody wants to add something.