Yes, all blades rotate at once. You can even remove the head cap and then switch it ON to see how it operates, but you should be opening it to only clean actually.
I think it is better you go for
this waterproof solution. It can even be operated with shaving gels and foams. It is a few hundred more than your budget, but really worth it. I am planning to upgrade to this from a long time, but haven't as the old one works just fine. Perhaps when it gives up I'll upgrade. You on the other hand have a choice to jump right in, and all for a few hundred more.