if im trying to do a quest turn in
 

thats MQ-able... do you think i will have enough time to turn in the no drops on my higher level then log quickly and turn in the final piece on the character who needs it?

this scenario is neglecting the risk factor of someone else giving the NPC other turn ins

more along the lines of.. is there a specific timer to get the last piece in

Yes, easy enough time to switch.