If a motor was installed and aligned, and after some time of running the motor became un aligned, what are some possible end results?

Broken u-joints?!?!?

you will burn up the donut for sure

I would imagine that it is due to loose motor mounts or bad stringers allowing motor to move? Bad results could be gimbal bearing, u-joint, or engine coupler failure. I suppose that in a worst case scenario the transom assembly could be ruined if things really let go. I'd probably figure out why it got out of alignment.

blown coupler, blown u joint that could take out the gimble and sink the boat... Why did it go out of alignment is the bigger question...

It was a motor mount for me. Came back to dock one day, boat half full of water. Ended up shearing drive coupler. Couldn't tell mount was broken, but saw bellows dripping water so on way to ramp, motor moved and sheared coupler.

Fiberglass never dry's fully.

It takes years but fiberglass can move. It can shrink and stretch and do all sorts of things. Even if properly bunked the fiberglass mounted stringers can move from the transom.
That being said , check your boat storage and trailer bunking. Also if it is minor it could be from just sitting for a long time.

A prime example. When you blue print the waves on the bottom of a boat. you can make the bottom strait as a arrow. Over time the waves can come back and require more blue printing once again. ( just an example)

What about engine damage? Any chance the misalignment would cause bearing/block/crank damage?

My direct experience is with a 7.4 MPI Bravo 3. The prior owner - we think- thought that the engine mounting bolts were loose. He proceeded to tighten them. As a result he knocked the engine out of alignment -- It tore up the coupler not to mention the drive shaft. It was pretty expensive to fix since I had all the rubber replaced, water pump, gimbal all while everything was apart.

Long and short - every two years I'm having the alignment checked along with the out drive serviced - u-joints greased. In fact my boat is at the shop as I type getting this done and winterized.

Even though we may have fiberglass stringers, mounts etc- boat hulls do move - something has go to give and an alignment check is cheap insurance to other bigger problems.

3pointstar