I have received miles from 5 US hotel stays completed in the past few weeks and all within the normal timescales of a few days since each check-out.

I also received miles transferred from my first BAA conversion within two days.

I don't expect the Avis points earned to hit the account for 6 weeks or so from previous experience and I will probably have to chase them as usual for the bonus 250 miles for booking with BA PP Amex.