A quick update on how long it took for miles (AAdvantage miles via Fidelity promo) and points (Ultimate Rewards via Chase Sapphire Reserve bonus) to post:
Chase: Applied for the Sapphire Reserve card on Thursday 11/17; got card on Tuesday 11/22; met spend by 12/7 December statement close date. 100,000 Ultimate Rewards bonus points appeared in my account on Sunday 12/18, BEFORE I had paid the statement balance which is not due until January. Wow.
Fidelity: I made deposit to Fidelity on 12/5; miles appeared in my AAdvantage account on 12/18. 13 days. Not bad at all!