The sail does cause supplies to be used. To calculate supply usage for a ship, it's (Total_Movement) * (Engine_Supplies_Used). So your ship has 10 movement, and the total supplies used by the engines is 6*10=60. 10*60=600, and your cloak adds another hundred. And it is supposed to use supplies, because technically, in the game, the engines are still "working".
Your design should work fine though, since you won't need to use the cloak all the time, and there's the occaisional binary and trinary system. So break-even without cloak, -100 with cloak (from reserves of 2300, 3000 minus max supply usage, for 23 turns of cloak). Then in binary systems you get +600 without and +500 with cloak, and in trinary +1200 without and +1100 with. Even with binaries and trinaries being scarce, you should be able to travel cloaked through at least 17 systems without running out of supplies, and add on all the nebulae systems
Of course, I would say your biggest worry here would be mines, not supplies