Insurance company doesn't care about the tag/registration. They only want to know if you bought it, and you're insuring it.

With a standard auto policy (not a collector policy), you typically have X number of days to add an additional vehicle to your policy, and Y number of days to notify them that you purchased a replacement vehicle. The former timeframe is usually shorter than the latter. However, it only applies to passenger vehicles. If you buy a commercial vehicle, a motorcycle, and RV, etc...you have to call and get a policy immediately, since none of those things are covered by your auto insurance.