Does Dropbox expect to be compatible with the new MAC OS when it is deployed?

They have been compatible with at least the last 7 versions, including Catalina, on the day they were deployed. I doubt the future will be different but time will tell.

Only they know for certain, but I'd guess that it will be from the number of Mac Users... but I wouldn't be in a hurry to install any new OS until it's had a few versions to work out the bugs.