Since he just recently started marking- you stand a good chance of stopping that unwanted behavior after the neuter procedure.
Although it is natural, I think you can also influence Max as to where it is acceptable to mark and where it's not. I would think that allowing it in some areas of the home, but not others would be confusing for any dog. So I just go with the "Don't do it at all" approach. I discourage any marking inside my house at all ( should I say, I try my best anyway...
) but outside is a different story. I generally let my males mark where ever they want- OUTSIDE. However, I also don't use pee pads inside my home, I just have mine go outside to do all their business. You may not be able to do that in your setting, so that may make a difference.
Someone else may be able to give you some better advice, but I do think that since his marking behavior is new, you can still put a stop to it. You might purchase or make a belly band or two just to be on the safe side and help put your mind at ease as to whether or not he is still marking after the neuter. Sometimes I still put belly-bands on my un-neutered as a test just to make sure he isn't being naughty indoors.
Best wishes with his procedure on Thursday. Try not to worry too much- I am sure everything will be just fine. When I one of my males was neutered, when I picked him up he acted as if nothing at all had happened. I had been a nervous wreck. To him it was no big deal.