Sorry for this rather elementary question...

I'm looking at booking hotels for an upcoming trip, booking via the Chase Travel portal and using Chase Ultimate Rewards points to pay. In a couple of cases, I'd be booking hotels in other chains, eg Marriott. When I book these stays, the site asks for my hotel loyalty program and program number. If I enter my Marriott number there, do these stays actually earn Marriott credits/loyalty points for a paid stay?

On one hand, these are indeed "paid" stays (since I'm paying with Chase points, not Marriott points) - through I assume what Marriott sees is it was paid via Expedia. OTOH, IME hotel programs tend to be stingy and will look for reasons to not award loyalty points when they can...so does payment via Chase/Expedia invalidate any loyalty points I might earn for this paid stay?

This is a somewhat unusual setup for me, I'm not looking to turn wine into water and convert Chase to Marriott here, I just happen to have more Chase UR points to spend (and I find them easier to generate than, say, Marriott points); I have less Marriott points. But I'm interested in staying at a couple of Marriott properties, and of course since Marriott is getting paid, wouldn't mind earning some Bonvoy bucks since I'll be staying there anyway.

Should I expect Marriott to credit me for staying there, or will they treat my booking that's paid via Chase/Expedia as some scam and give me the stinkeye and the bum's rush? Thanks.