Yes, I’m certain it would be possible to do this. I’ve thought about doing it, but haven’t written anything, in part because it would be a significant effort to do bidirectional synchronization in a robust way and I don’t have a need for it myself. (I’ve resorted to tagging only in DEVONthink.)
To @chrillek’s good point, an important issue is how to detect that tags have been changed in one or the other application. In DEVONthink, one could probably find a way do it using Smart Rules, but I don’t think there’s a way to (easily) get the events in Zotero. It may be easier to sync on a schedule or on demand.
Another problem is that tags in DEVONthink can be hierarchical, but not so in Zotero. If you add a new tag in Zotero, it would require some scheme to figure out what to do when automatically creating the corresponding tag in DEVONthink. Similarly, you’d need to solve what to do with the DEVONthink tag hierarchy when writing them into Zotero records. These are not insurmountable problems, but you can see how the complexity is escalating quickly.
(Incidentally, @stighagen if you have not already seen it, you may be interested in an application I wrote to use Zotero and DEVONthink together. I also wrote some notes about my setup in a wiki associated on GitHub and there were some past postings in this forum, notably this one.)