It seems like an easy temporary fix for this would be to open the pdf in another viewer such as Xodo, do the annotations there, then read it back.
In fact the android client already has half of this: The “share” button (or share followed by Open) can open the pdf in another viewer, where annotations can be made.
All that is needed then is some easy way to read the resulting annotated .pdf back into paperpile from the android client.
Thanks for the request, @paperbrain. Some other users have also requested this over the past few months so the matter is on our radar, now with your +1 as well on our internal tracker.