Do you have a gen2 Tesla Mobile Connector? Then, yes, those are the adapters, you’d just need the NEMA 5-20. If you have a generation 1 Mobile Connector, then Tesla sells a 5-20 adapter for that one too. You can use the supplied 5-15 adapter, but in a modern hotel, those external plugs will all be 20A, so you’d get a faster charge with the 5-20.
I just looked at google images of that hotel. I’d give them a call and see what they say about plugging into the external power plugs. Or just go ahead and do it.