I have some real punky but beautiful logs that I cored for multiple bowl blanks with wall thickness of about one inch. Will cactus juice work on bowls? If I vacuum in cactus juice, do I need to wrap the entire bowl in foil and bake?

Yes, Cactus Juice will work fine on bowls.  It may get expensive, though, due to how much resin they will take up.  Since stabilizing punky bowls is primarily just to to make them turnable, I would suggest just getting a large enough container and just soaking the blanks.  In my testing, punky wood will typically double in weight just by soaking.  This will not be as well stabilized as if you used vacuum but for the purpose of being able to turn and finish them, it will be just fine.  They will be hard and turn without tear out, they just may not be as resistant to moisture as a vacuum stabilized blank.  The advantage of just soaking is you will use a little less resin and you don't have to try to get a large vacuum chamber. 

No, you do not need to wrap them in foil.  The primary reason for wrapping in foil is to contain the mess when some of it bleeds out (part of the process) and to allow you to put more blanks in the oven at one time.  If you do not wrap them in foil, be sure to not stack them on each other or you will end up with a bunch of bowl blanks glued together!  Also be sure you have a good drip pan under the blanks to catch the bleed out and prevent it from getting all over the inside of your oven!