Is it possible to just use a headset's mic but keep the phone's ear-speaker active?
Definitely not possible, the audio routing is something of a mutually exclusive/flip-flop principle.
If the headset is plugged in, the routing goes to the headset and is taken away from the in-built ear-piece. Vice-versa, if no headset is plugged in, the in-built-ear piece is used.
Likewise, for when during in-call without headset, audio routing goes to both ear-piece and mouth-piece, no other mp3/music cannot be played. For vice-versa, when no calls are happening, audio is routed to the speakers...
That shows what is actually involved in, what is known as "Audio routing" and is very complicated process hence the emphasis on mutual exclusivity/flip-flip operations of the audio fundamentals.
After some further research I think it's not possible.