Largely yes. fdbmonitor and fdbserver have no particular requirements that would require being able to run anything as root.
My largest concern would be that you’d be unable to raise the file descriptor limit, which can cause problems as seen in All Coordinators Crashed At Same Time. However, if you know for certain that you’ll never exceed ~500 clients and servers combined, then it shouldn’t be an issue.
The question also implies that you’re running on a server that you don’t have control over, and FDB doesn’t quite do the best at handling disks that may spontaneously start to fill up with files that FDB doesn’t control.