Board Thread:The Quarters - Q & A/@comment-167.220.2.198-20190412163711/@comment-25085701-20190412165920

I do not believe so, since Habitica is a query based client -- stuff doesn't happen unless you or someone in your party sends it an event (clicks something), and the latter is only for things like quest invites. So you won't get those sorts of granular push notifications automatically.