100% variable depending on property policies. As examples, some properties adhere strictly to an "on arrival" policy, while others will upgrade several days in advance, particularly for regulars.

I would never call and ask for a comp upgrade. I will ask about room assignment in person at check-in, and if they haven't upgraded me, ask if they have something better available. In general, I have very good experiences with Hyatt upgrades (without having to beg for them).