MJM, not all of the LRCT holdings are open to the public. Click here for a list of those that are open and accessible to the public:
http://www.lrct.org/public-access.html
The acreage on Rattlesnake Island is not on the list of publicly accessible areas. The remainder of Rattlesnake Island is held by private landowners, and therefore the entire island is private. Docking at any dock on that island would be considered tresspassing, I'm sure.
For a nice island hike on LRCT land, try Stonedam Island!