I can answer it for my own: it´s not allowed
Here’s what I’ve been trying to do:
I have two user working at the terminal server. The first one has running KeePass and Firefox with the Kee plugin normally (default settings).
Then the second user starts KeePass (also default settings in the KeePassRPC Options) and for the first time Firefox with the activated Kee plugin. The browser opens the Kee Authentification tap and in the same time you will get a second window from KeePass with the keyword. Nothing new – you know that.
Now I change the port RPC Options e.g. to 12540 and do the same in the Kee settings. After that the Kee Authentification tap opens again, but there is no keyword window from KeePass.
Maybe this will help narrow down the problem…