Nah, you can link your Nintendo account to your profile on multiple Switches, the only problem is it differentiates between the main and secondary consoles. On a secondary console, you need internet access to access any download data that's tied to the Nintendo account (such as digital purchases, but also stuff like the Pocket Camp extras, IIRC), and you can't share any digital purchases with other users. As long as you have stable internet and don't have digital purchases you want to share with other users, it works fine. And yeah, from what I found, only the resident rep can invite villagers, but if the first account is yours and doesn't already have a Nintendo account linked to it, you should be able to just add that one.
The items you get in the mail are only for the last update, not for all of the updates. They're all reorderable, though, so you can still buy them.