Have you attempted to contact them. I found them on chat and was able to setup a mobile tech to come install them. The “Chat” button is elusive on support and only shows when they have agents logged in and ready to chat. If you don’t see it, you could try calling as well.
Badge, probably. Spoiler, no they wont ship it. You might be able to work around it by scheduling a mobile appointment to put it on, then when the mobile tech gets there telling them you will just take it.
The issue with that is, they still dont fit right (I am going in for my third try to get one to stick right), and if they dont install it, and then you want to take it back cause it doesnt fit, if I were them I would be like "thats because you didnt install it properly"... even though that likely isnt the case.
I specifically had tesla install mine, because I was afraid they would not fit, and I did not want ANY question on improper installation, and the part still does not fit properly. The service center thinks its the spoilers... I happen to think that its because the trunks themselves are not all the same tolerance but /shrug.
Anyway, tesla has spoilers and badges. Put in a service appointment to get one installed, then choose what you want to do during your installation appointment, keeping in mind what I said above about issues you could have if it doesnt fit or, STAY fitted.