Unless everything I think I understand about tulpas is wrong, this is at the very least significantly harder than just thinking yourself smarter without one. All the idea generating is done before credit is assigned to either the "self" or the "tulpa".
What there ARE several examples of however are tulpas that are more emotionally mature, better at luminosity, and don't share all their hosts preconceptions. This is not exactly smarts though, or even general purpose formal rationality.
One CAN imagine scenarios where you end up with a tulpa smarter than the host. For example the host might have learned helplessness, or the tulpa being imagined as "smarter than me" and thus all the brains good ideas get credited to it.
Disclaimer: this is based of only lots of anecdotes I've read, gut feeling, and basic stuff that should be common knowledge to any LWer.
I'm reminded of many years ago, a coworker coming into my office and asking me a question about the design of a feature that interacts with our tax calculation.
So she and I created this whole whiteboard flowchart working out the design, at the end of which I said "Hrm. So, at a high level, this seems OK. That said, you should definitely talk to Mark about this, because Mark knows a lot more about the tax code than I do, and he might see problems I missed. For example, Mark will probably notice that this bit here will fail when $condition applies, whi...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.