A: Yes, on most instruments, we can. On standard tuning, the bass strings group is nearest your face, and in ‘uncrossed hands’ the instrument is restrung so that the harmony strings group is closest to your face and bass strings group furthest. The benefit is that your left hand on the left side of the fretboard can go all the way up and down the bass strings on the left side of the instrument without running into your right hand.
It can slightly change the sounds coming out of the pickups because pickups are not spaced identically on the ‘bass’ and the ‘melody’ side, but this shouldn’t be much of an issue.