For the benefit of others while I got one initial user to work using OmniPresence and an Apple OS X server acting as a WebDAV server a second user would not work.
Even ignoring OmniPresence which might have tougher requirements, the Apple webdav server is well known to be problematic even using the Finder as a client has problems. (CyberDuck manages ok.)
I can however report that a NetGear ReadyNAS running 4.1.13 software works fine. I have several users running with no problems and even have several of them simultaneously accessing the same shared webdav share as well as their own private shares. This apparently contrasts with Synology NAS servers which according to a previous report do not work with OmniPresence.
I have not tried a newer generation ReadyNAS boxes running e.g. 4.2.x or 6.x software since I did not need to. The old one I used was more than powerful enough for this job.