No you do not have to bake the popcicle sticks. Baking wood is only for wood that has been outside to make sure that the wood dries out after scrubbing/boiling process. When I used Kool-Aid I added less water and more Kool-Aid to make the dye a bit stronger. I didn't really measure it out.. just sort of eyeballed it.
I put mine in a spray bottle & mist the wood with it, then I lay it out to dry. No reason to bake it unless you're drenching the wood. You bake it so it doesn't mold.
I poured one packet into half of a standard spray bottle.