Yes, they do. If he's otherwise well in himself, then he's probably fine.
I once had a hamster who started having the most enormous balls, concerned I took him to the vets who said they might be swollen (in hindsight, they didn't have a clue), so they gave him an injection and advised me to give him a could compress every day. I did this diligently, but his balls did not get any better, in fact they seemed to be getting worse.
So my parents took the hamster to their vets, and the vet almost fell about laughing when he heard. Turns out, hamsters keep most of their balls inside of them, but my hamster was lazy, and used to let them out. Turns out he quite liked the cold compresses, so I stopped them immediately, and strangely his balls got smaller again. From time to time, he used to let himself swing loose, but held them in most of the time.
Our current hamster likes to sit on his balls and use them as a table
.
The vet told us, in human terms the proportion of a hamster's balls on a human would be like having them down to your knees.
They are generally huge.