CaptainJay mentioned our boat, 6'5" per manufacturer. I hug the south side of the channel going in/out. I anchor off of Setting Point in 10'-12'. The main anchorage with mooring balls has been silting up this past year, so we don't even try in there. In November we anchored east of the last red channel marker and had a half dozen boats as company.
7'? Its possible, but I would double check the draft, depth gauge and tides and anchor at Pomato Point.
I remember a blog post by Zanshin about his shortest ever visit to Anegada.
Cheers, RickG