Reverse characteristics of power MOSFET
Here are the (simplified) rules by which a N-channel MOSFET obeys:


If the voltage between gate and source is grater than the threshold, the current can flow between source and drain (in either direction).
If the drain voltage is lower than the source voltage, the current flows from source to drain, even if the gate is not triggered (due to the body diode - and there is a bit of voltage drop).


That is all. Now, here is how it works in your situation: Since you want reverse voltage protection, the MOSFET can't be in the other direction, because the body diode would allow current to flow, powering your device with reverse voltage. So the MOSFET has to be that way. But because we want to avoid the body diode voltage drop, the gate is tied to the +BAT, so the FET conducts when the battery is the right way around. Then, the result is the same as if you had a small resistor (the MOSFET RDSon) in parallel with the body diode, thus reducing the unwanted voltage drop a lot.

There is no reason this should have a bad impact on the MOSFET. Whatever the direction of the current between drain and source, the MOSFET can handle it (provided you're under its absolute rating).

Last thing: you're worrying about power dissipation. The power dissipated by the mosfet is just Vds times the Ids current (ignoring the current through the gate). Or, put in another way, RDSon * Ids² when it conducts. You can estimate it very easily. And, once again, it doesn't depend on the direction of current (a switched on MOSFET doesn't conduct less well in the reverse direction - in fact, it will even conduct a bit better in the reverse direction, because of the body diode in parallel).