Can gradient boosted trees fit any function?

For neural networks we have the universal approximation theorem which states that neural networks can approximate any continuous function on a compact subset of $R^n$.

Is there a similar result for gradient boosted trees? It seems reasonable since you can keep adding more branches, but I cannot find any formal discussion of the subject.

EDIT: My question seems very similar to
Can regression trees predict continuously?, though maybe not asking exactly the same thing. But see that question for relevant discussion.