All states DMVs are supposed to share all ticket/conviction information. If they do their jobs, then, it should show up on your CT record. CT makes their own rules about whether they give you points - if the offense is one that would carry points in CT, they could give you those points.
Your insurance can pull your DMV record whenever they want. If the points show up, or even just the out of state conviction with no points, they would be within their rights to increase your rate.
Mr. Esten is correct. There is an Interstate Driving Compact where any moving violations received while out of your home state are supposed to be reported to your home state DMV and 2 points assessed on your license.
There is an interstate compact that requires New York to report your speeding conviction to the licensing authority in Connecticut. According to the compact, the licensing authority will impose the same sanction you would have received had you committed the same offense in Connecticut. You can be assured that your insurance company can and will learn about the infraction. They devote considerable resources to monitoring the driving records of their policy holders. Wish I could offer you better news. Good luck.