In most states plates stay with the vehicle. The registration is changed in the computer, and you get issued new plates and stickers in your home state, but until then nothing changes on the outside of the vehicle. Cops won't think anything is weird. To be legal, you should get a trip permit.
If I bought in a state where the seller keeps the plates, OTOH I would also put a paper sign where the (missing) license plate goes that said, "I have a trip permit". In case anyone wonders :B.
Insurance you do with a phone call, so you can do it from anywhere.
