No, the check valve is in addition to the air admittance, or anit-siphon or backflow preventer valve. The anti-siphon valve is located in the high point of the system, and open to atmosphere thru its "hat" when no pressure is present. This breaks the vacuum necessary for siphon. However, this also allows downstream air from the black tank to flow upstream into the compartment where the anti-siphon valve is located. When pressurized, the anti-siphon valve closes to allow water to flow thru the system. In my system, the flow is upwards thru the anti-siphon valve, and horizontally out of the anit-siphon valve and thru the check valve.
On my rig, immediately downstream of the anti-siphon valve is a 1.5" nipple, which looks like a short section of fitting, which is actually a spring-loaded check valve. Inside this piece is a valve that is normally closed, and opens when presented with about 7 lbs of pressure. It allows flow out of the anti-siphon valve and to the system, but closes when flow is discontinued to prevent poo smell from back-flowing and exiting thru the anti-siphon valve's hat. The check valve alone would stop, but not break the siphon, an anti-siphon valve is required by code in any system that presents a possibility of cross contamination, like a black tank flush system or your home sprinkler system.
On my rig, the anti-siphon valve is a fist-sized brass inverted 'L' shaped device and the check valve is a 1.5" gray plastic nipple coming horizontally out of the inverted L, all located behind the bath vanity drawers for convenience. If you have two right arms, it's very easy to get to.