I used to work in a lab with a lot of birds (like, several hundred). There was no way possible to keep the place entirely clean of bird seed and other edibles. We had both roaches and mice (not to mention other problems). I never worried about bringing the roaches home, but then I wouldn't have brought my bags into the bird rooms anyways. The mice we trapped humanely and released.
I'd much rather deal with mice than roaches. I have to admit, if I had one in my house (and the two cats didn't get it), I'd probably buy it a cage, catch it, and make it a (not exactly tame) family member.