I'm taking each receptacle is going to be a separate circuit. If it is a MWBC (2 hots sharing 1 neutral ) then no, you don't break the neutral off. But if you are having a separate neutral for each hot, then you would break the tab off. You need to feed it with a 2-pole breaker or 2 single pole breakers with a handle tie, so when you you shut one circuit off, the other de energizes also. This is a code requirement for safety
When you say that you are using nearly all 15 amps, what kind of loads are you plugging into it