I don't think its such a good idea. I doubt the microscopic marine life you collect on Eastern LI will do well in a reef tank with much higher temperatures. Once these organisms start dying off you're gonna have all sorts of problems.
Seeding a nanotank with NutriSea or another real saltwater product is not such a bad idea. These products go through UV sterilization so they are safer than a bucket of water that we could collect from the ocean.
From what I've read over on nano-reef.com (which is mostly people from California) people go out a few miles to collect water to use in their tanks.
In my two years experience with a nano reef(24G), I have found that if you use NutriWater or Real Sea Water(PETCO), you will have a good foundation, especially to start. I wouldn't use the water out of the sound.
I actually use it for water changes as well. My studio isn't big enough for a RO unit yet, and usually 1 5 Gal box is sufficient for a water change every 14 days. The price factors out to be the same if you were to mix your own.