Grammatically correct? No, but it's something you're going to hear anyway.
- Why is it not correct? See parallel structure. The grammatical
structure of "have been for drinks" and "chatted with my
friends" should be the same, which is, it should be in the same
- Why is often said? Because saying "I have been for drinks, and at that time (or "and while I'm drinking,"), I chatted with my friends" is very long. In speech, often what can be assumed will be. So the logical conclusion is that the two things happened at the same time, even though the shortened version isn't explicit in saying so.
Another way to say this, still short and also correct, would be:
I went for drinks and chatted with my friends.
If the "have been" is intended to imply "I just now did this thing in the very recent past," you could go with:
I just went for drinks and chatted with my friends.
I went for drinks and chatted with my friends just now.