if a quarterstaff counts as a polearm, then a polearm.
according to wikipedia...
"A quarterstaff (plural quarterstaves, also short staff) is a traditional European
pole weapon and a technique of stick fighting, in use from the medieval and throughout the early modern period, into the 18th century."
the words "pole weapon" and "pole arm" are synonymous,
so yes a quarterstaff counts as a pole arm