I am not sure if my experience applies, but I live on Cayuga Lake so the same NY laws might apply to Lake Champlain as well, at least the NY side of it. The rules on my lake say that you can put structures up to 100 ft. from shore but more than that is considered a hazard to navigation and the authorities wont allow it. Having said that, I have never heard of any enforcement of this and my mooring is sometimes more than 100 ft. and sometimes less depending on how high the lake level is. However, it might matter that I own the shoreline where my mooring is - I dont know if there is any rule to prevent somebody else from mooring in front of my house but I do know it would make me very unhappy if they moored a big honking boat right in the middle of my view, and also interfering with my own ability to tell friends to come over and anchor out. Doing it in front of state owned land would almost certainly get you in trouble (the state park police are pretty strict) but there are stretches of undeveloped lake front where nobody would know the difference I am sure.
On the other hand, if Champlain is anything like Cayuga the lake bottom for the most part is pretty rocky. You would need to have a pretty good mooring system to have any confidence. The old fashioned method was to heave a couple of chained-together car engines in the lake but that wasnt very environmental so now people chain together garbage cans full of cement unless they are lucky enough to have a gravel or mud bottom.