It's not a moving violation so it shouldn't. It should have as much impact against your insurance as a parking ticket. To find out for sure, you could always call your insurance company. Or you could call any other insurance company and ask a "hypothetical question".
Most courts have some sort of a waiver if you can prove that you got your plates registered within a certian number of days after you got the ticket. I think its like 10 or something. Your tags can't have been expired for more than 60 days, usually, to qualify for the waiver. You can call the court house to find out. The waiver fee is like 10 bucks or something minor like that. You could look into that if you are interested in keeping it off your record altogether.