Neither the Warranty Information Booklet nor the Service and Maintenance Guide say anything at all about a six month battery check, no matter which service schedule you are following for your car. The Service Guide calls for an annual check, regardless of mileage. The Warranty Booklet says the same thing, and that the two at 12 months and 24 months are free.
It happens that I took my car in for some service today and asked what my records showed, since I had taken the car for the annual service last spring but never got a battery report. The interesting response I got back was, "Yes, it shows that you got your 9 month to 15 month check." My inference from that is that they give you a three month leeway in either direction. Anything outside that range you would have to pay for, and could cause warranty problems.
NOTE: That's my inference. Nissan didn't tell me that.
Ray