Only in a very specific sense of "exist". Do hallucinations exist? That-which-is-being-hallucinated does not, but the mental phenomenon does exist.
One might in a similar vein interpret the question "do tulpas exist?" as "are there people who can deliberately run additional minds on their wetware and interact with these minds by means of a hallucinatory avatar?". I would argue that the tulpa's inability to do anything munchkiny is evidence against their existence even in this far weaker sense.
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I was taking a statement from this great-grandparent post and surrounding posts at face value
By "do something munchkiny", I meant these "obvious ways to exploit having a tulpa", presumably including remembering things you don't and other cognitive enhancements.
Why do I think they can't? Because the (hypothetical?) domain experts say so.