You mean a generator on the trailer wheel. Say it is always on and working, generating power while you ride. The power you get back from the system is always equal to the extra power needed to pull the trailer, You won't go any farther than you would have without it.

Now if you use a powered motor, it's the same except when you brake. If you have a circuit that puts the motor in regenerative mode, it will brake your bike/trailer. The energy that would have been used in your regular brakes is sent back to the battery, That's the reason for using a big direct drive motor with regenerative braking in a cargo bike. It recovers some energy that would have been wasted as heat.

Justin from Grin Technologies in Canada (grin.ca) has run solar powered recumbent ebikes with regen across the Alps from France to China knows his stuff. He says you get 10% more range in the mountains,. He will sell you motors you can put in the trailer and the electronics too, Probably cost around a thousand dollars USD, Read his web site and see if it makes sense, I think he's an honest guy.

Me, I don't need the range. I like my ebikes simple and light. Regen doesn't work for me at all. I like going faster downhill and coasting as far as I can before I need to start pedaling again,