Wine v1 is considered stable. "Stable" is always a bit relative and I think that because of the nature of Wine and its complexity as well as the always-changing applications running on it themselves it would always be somewhat touchy.
That said, I think that if you go by the different classes of application compatibility in the Wine App DB and only use Gold ones then one can probably safely say it is reasonably stable. The Wine community is great and I'm sure will be a great help.
For multiple workstation, mission-critical use I think you would be better off going with a commercial spin-off of Wine like CodeWeavers CrossOver Linux and have the benefit of commercial support.