Backing off a trailer outboard damage

Is it possible to damage an outboard from having to run the motor hard in reverse to back off the trailer? Like break the tilt and trim unit or damage the transom. I have a Yamaha 4stroke 50hp high thrust model on an 18ft G3 and it kicks up a little sometimes when I'm trying to get it off the trailer

No

Not if the transom is in good shape. If it is rotten, yes.

Back the trailer in the water more?

this

Not really good to start it then mash on the throttle without warming up. Back in further.

You might try backing in farther to get the bunks wet & then pulling back up. My aluminum boat (Tracker ProTeam 170) tends to stick to the carpet runners, but if I get 'em wet I can tie a good rope to the boat and tie the other end to the trailer or give it to my wife. Then just back up and stop quick - she comes right off and the rope unwinds and catches the boat. After the boat comes off, I just pull up enough to keep the boat from drifting and secure the boat to the dock, then park.