Am I considered fulfilling postdoc duty in this situation?
I don't see any ethical consideration as long as your PI is happy and you aren't violating any specific contractural arrangements from your funding. I think that is unlikely. Whether you need to list the PI or not is a different question, and depends on your field and somewhat on the PI. If the PI can help in your future career, it would be good to consider them as author, but my opinion is that would imply that they contribute something. 

But authorship of PIs and supervisors varies by field. 

And yes, acknowledge the grant and its funders.