My guess would be yes. If there are no points listed on the second page, you probably wouldn't get any. I've noticed the the benefit of the points often comes at the trade-off of a non-refundable reservation.
I would estimate about 90% of the rooms I've booked through AAHotels only offered non-refundable options.

You could always book the refundable reservation and cancel if it is not what you expected. It will clearly show on the receipt (which you can view immediately) how many points the reservation will earn. But my guess would be zero if it doesn't say so while you are making the reservation.

Another thing I notice is that the cancellation policy (or in my case "non-refundable" policy) seems to vary by city. And I am unsure if RocketMiles would be any different... I haven't checked.