Nah I don't think so. I think it's just a clumsy wording for "add another device," but they're all "equal" in the sense there is no real "primary" or "secondary." At least, I haven't been able to tell the difference yet myself if one is a primary haha.

The only difference I'm aware of is, if you're only using one device messages get deleted from the server immediately after download and stored locally, if you're using "multi-device mode" then it depends on your server iirc but default is they get deleted off the server after 30 days (in case one device is say a laptop that isn't always running, so they can sync, presumably you boot/connect it at least once a month I suppose).