Has anyone used a 15" spare after 16" conversion?

The short answer is yes. :)

Yes I have, did so with a 225/75/15 load range D when one of my 225/75/16 load range E tires lost part of it's tread, towed it some were around 150 miles to were I was going to stay.
The trailer came with the 225/75/15's.

And heaven forbid you should have AWD. If there's a differential, limited slip or standard, on that axle, you've got a problem.

If it's on a non-driving wheel (trailer for instance), it's fine. If it's on an axle with a limited slip differential it's very possible you'll burn out the clutches. Some types of limited slips are more picky than others, so be careful.

Moved from Technology Corner

Should be fine. Shoot- I've chained axles up with no tire (or hub, for that matter) for short distances.

It will be fine. As donn said capacity must be sufficient for load. It's half in inch or so smaller radius depending on tire manufacturer so it's going to drop that end of that axle by a half inch. In theory as one end of an axle drops and the other stays the same you will be applying a twisting action or side force to the dogbones and pivot bolts.

It's also not like putting 2 different size tires on a drive axle and having the differential gears spinning at different speeds.

You also already realize that it should be for very limited miles.

No reason not to as long as it has the load carrying capacity to handle the load AND it is the same diameter as the current tires on the ground.