If forced to bug in, it's reasonable to make use of edible animals when the opportunity presents; but IMHO to rely on hunting means that your preparations have been grossly inadequate. In any kind of extended situation, the bulk of your calories will not come from meat; they will come from the beans/rice/lentils/oils/grains you have stored.

People who live well out into the country will of course have better luck (more game and less competition). But people in or around urban areas better not rely on this.

Urban game will vanish in no time. And if you have enough mobility to go farther afield, that means you have gas to spare and the roads are open. You're not really "bugged in" at that point. You don't need to go hunting wild game, you need ready cash and/or tradeable goods; you need to draw on your rural contacts to buy stored wheat/barley/corn or take a share of a beef or pig.

You might also consider putting some rodents to work for you, converting plant material you can't eat in to stew that you can. Rabbits? Meadow voles? These breed rapidly and can reliably supplement a survival diet, even in a suburban back yard. Agriculture beats hunting every time; that's why humans switched.