According to an anonymous poster on 4chan:

Pretty much everyone that has them has reported that they do a lot of interesting things that are just plain impossible for a puppet, from memory access (can retrieve a lot of lost memories, or even remember entire books in perfect detail) to reported dream experiences to them joining you in your dreams and have their own experiences.

I proposed a simple experiment to test if the tulpa is its own being: have the tulpa work in parallel with you own some problem, for example, some advanced math. You would be focusing all your attention on something specific thus having no time to work on the problem, while the tulpa does just that. If the tulpa succeeds, you can conclude that it's its own independent mental process separate from your own.

One person who was asked to performed this experiment reported some success that's just not feasible for normal humans. Failure was reported for those that parroted (regular imaginary friend).

I plan on trying this stuff for myself and experimenting, then I will know for sure.

Even if the poster is straight-up lying, this is a clever munchkin use for tulpas and interesting idea for an experiment (although I admit I know practically nothing about the typical performance patterns with that kind of problem-solving).

also, a couple of other points:

• Psychologist T. M. Luhrmann has suggested that tulpas are essentially the same phenomenon as evangelical Christians 'speaking to God'. I can't find any evidence that evangelicals have a higher rate of mental illness than the general population, so I consider that a good sign on the mental health-risks front.

• If you are worried about mental health risks (EDIT: Or the ethics of simulating a consciousness!), then you should probably treat guides to tulpa creation ('forcing') as an information hazard. The techniques are purely psychological and fairly easy to implement; after reading such a guide, I had to struggle to prevent myself from immediately putting it into action.

ETA:

Some prior art on the parallel problem-solving idea. I'd say it fairly well puts to rest that munchkin application. In terms of implications for the mechanics of tulpas, I'd be curious how teams of two physical people would do on those games.