And would an AP wait to transmit if a device were broadcasting to another AP on the same channel, due to CSMA/CA?
ARQ and CSMA/CA serve different purposes.
ARQ (and similar mechanisms) ensure reliable communications, giving confirmation that data has been received correctly. Received packets are acknowledged by the receiver so that the sender knows they have in fact been received.
CSMA/CA is a method of sharing a common media (radio channel) among multiple senders. It allows multiple, independent senders to use a media where only one sender can transmit at a time. Each sender waits until the media is idle before transmitting.
And to answer your second question: Yes, that's the whole point.