I had my surgery 3/26. Everyone is different, as I found out. While some have no hunger and no cravings, others still do. I happen to be the unfortunate one that woke up hungry still crave food. However, when you are recovering from surgery, perhaps watching more TV than usual including all the food commercials, it's kinda hard. At least for me. The full liquid is probably the hardest part, and I have confidence that as I get to the next stage, it will get easier.
I might still get hungry, but I also get full with very little. After a few months, if I have a tremendous craving for something, I will be able to eat it, but only a very small amount. Portion control is a huge help.
Bottom line, imo, is that no. The surgery may not rid you of obsessive thoughts, but again it could! If not, what it will do is give you time and tools and a head start to tame those thoughts. After all, you may want a big fat cheesburger, but your stomach will make you pay dearly if you have it! So it's not so much 'you shouldn't', but more 'you physically can't'.