Sailing the St. Lawrence, then proceeding down the Atlantic coast of the US will definitely be an interesting trip, and you'll be sailing along some of the most beautiful coastline in the world doing so.
, the route is feasible, and shouldn't pose too many problems, although I don't know how much sailing you'll be able to do on the St. Lawrence to the northern Atlantic.
I don't believe draft—either air or water will be a major concern. However, at the mouth of the St. Lawrence, tidal currents and tide levels will be. If they're anything like the nearby Bay of Fundy, the tidal changes will be relatively massive compared to further south—on the order of 20-30' IIRC. However, I don't have any personal experience with sailing the St. Lawrence, so I could be wrong. (For full disclosure, I haven't sailed the Bay of Fundy either, but I've been there and seen the tide change...very impressive, and damned dangerous if you're not careful).
I'd imagine that June would be rather nice, if a bit cool on the St. Lawrence, and fog will be a factor along the coast of New Brunswick, Nova Scotia and Maine. Nights can be pretty cold that far north as well. Might be worth packing the fleece... Since you'll be sailing on those waters, it might also be wise to pack either drysuits or "gumby" survival suits, in case of an emergency.
If you want, I can run this through VPP and see what it says for distance, time, and time spent motoring and such.