Does a verb phrase always function as a predicate?

(1) [What is obvious] is that we are choosing a new path.

(2) I took a train heading north.

Yes, in (1) "is obvious" is the predicate in the bracketed NP -- a fused relative construction meaning "that which is obvious".

And in (2) "heading north" is predicate in the bracketed gerund-participial clause modifying "train".

But VPs are not always predicates. They can occur as attributive modifiers in NPs, e.g. "a sleeping child", where "sleeping" is not a clause and hence "sleeping", although a VP, is not functioning as a predicate. The rationale behind this is that the structural possibilities are too restricted to justify a clausal analysis: you can’t have a subject and you can’t have a post-verbal dependent.