A lot of people do this, enough that at some points it's been a fashion on fixed gears. All you have to do is put the cable through the normal way with the head resting on the back side of the lever, where it will sit in the housing slot. There are some levers that are made to accommodate the cable head there snugly using a removable plastic bit.
The main reason to do it is if you want a flatbar style lever on a clamp diameter they're not otherwise available for, I.e. 23.8, 25.4, 26.0, and 31.8mm, and you either don't want to mess with forcing/adapting a standard 22.2 lever or there's no real way to do it, as in 31.8. If you can just use a 22.2 bmx lever, that's what I would tend to do, because they're generally better brake levers.