My experience with quality Hyatts is that the upgrade has been allocated long before you are talking to the front desk. Therefore a welcome note is waiting for you with an amenity.

The only issue with arrival time is your allocated room not being available yet, and having a discussion about whether you'd rather take whatever room is available at the time of your arrival.

Trying to DYKWIA to a suite upgrade before another DYKWIA guest similarly abuses the front desk clerk - when the hotel didn't intend to upgrade any Globalists - is too full of variables to worry about.