It depends on the supplement. Some are better absorbed on an empty stomach, while others are better absorbed when taken with food. Best to follow what it says on the bottle -- and don't worry about it if it doesn't say.
A green food supplement that I recommend often that is high in protein instead of spirulina, is a blue/green algae product that comes in capsule or fresh, frozen form (the powerful stuff;-) It's called E3Live or E3AFA and it is made by a company called Vision.
You can order it directly from the company by calling: 888-800-7070
Tell them I sent you and maybe someday they will reward me for it!
That would be a really good one for you with the sugar cravings, etc.