I’ve booked a couple of those “World of Hyatt eligible” hotels through the Chase Travel portal and yes, the qualifying nights did post for me. It took a bit longer than a direct Hyatt booking, but they showed up and counted toward status.
The key is that it has to explicitly say World of Hyatt eligible in the Chase listing. If it does, you should get elite night credit and points just like a normal Hyatt booking. If it doesn’t say that, assume you’ll get nothing.
I’d still screenshot everything and keep the folio just in case you have to chase missing nights, but in general it does work
