Usually no. Wine is pretty stable by this stage. But, like always, that's not a guarantee. I say that because of the version numbers. The standard numbering system is 'Program-x.y.z' where
- Z = bugfix type release, nothing meaningful added.
- Y = Feature additions.
- X = Break in compatibility.
So when you go from wine-5.x.x to wine-6.x.x, that's a compatibility break. I did it more than once, and got away with it each time. But the more features you're using, the more errors are likely. It would be worth consulting the ChangeLog to see what actually changed. IIRC, some directory names changed or moved about.
Upgrading just updates the binary package in linux. When you start wine, it notices that everything in your user account is out of date, and grabs the latest kit. So start it with 'winemine,' or something innocuous.