I've made (mostly useless) Choice Gold two years running with 10 stays/year without a single Choice Rewards points posting, as I've always had them go to airline miles.

Stays booked through one of the Choice Hotels websites definitely count for stay credit while you earn airline miles, if you book them while logged in with your Choice Rewards# with your profile set to earn on your preferred airline before you book the stay. They don't show up after the stay in "Stay Activity" but they do increment your Stays counter for Status.

Perhaps if you just give your FF# at the front desk, it doesn't count for credit because the hotel just puts in your FF#. The critical thing is to have your profile set up in advance for the airline you want, before you book.