[Salem13]

It wouldn't hurt them physically but would likely freak them out as others mentioned. However I can see some benefits in some cases.
For example if you have a male dwarf hamster it could be a good idea to get them as comfortable as they can with you looking at their stomachs, which could be them laying on their backs. This is because their scent glands are on their bellies and can get impacted and even infected in some cases. My last male dwarf happened to get an impacted scent gland fairly regularly and my vet told me to regularly clean it for him with a cotton bud dipped in lukewarm salt water. He wasnt necessarily trained to be comfortable on his back but over time didn't freak out as much when I tilted him backwards.
Dwarves as a whole also tend to have more difficulty keeping their nails short and it can be easier to trim them if they're on their back or in a sort of vertical position.
It's also a very good idea to check your hamster over for changes or injury fairly often and the stomach is generally the most difficult to see- hamsters are very squirmy as I'm sure you know. Training them to be less squirmy or be comfortable in the aforementioned vertical position could possibly help you have an easier time.
Finally if you have a hamster that has frequent vet visits it could be useful to get them more comfortable with it too. Generally the vet will be handling them and turn them over while doing so. Though you can also just attempt to get your hamster more comfortable with handling in general, its still helpful if theyre less squirmy when checking specifically the stomach.

So, in essence: attempting to train them would likely freak them out but if you have the time it could be a good idea trying to get them more comfortable with exposing their stomach, whether thats being held in an upright position or on their back depends on the hamsters comfort.