Following answer assumes you've got tires with directional thread (if you flip the tire 180 the pattern will mirror upsidedown).
Among other duties, tire threads are responsible for "pumping" the water out from below the wheel when you drive through it. If you reverse the directional tires then the water will be pumped to under the wheel, effectively providing you with aquaplaning. That can badly affect handling irregardless of drive-wheels positions (fwd or rear).
Rear end is useful not only for braking, but for keeping vehicle stable on the road, allowing the car to take corners. Think of it, if you remove rear end traction and have only front 2 wheels, the car will spin (see YouTube for "half a car" examples).
However if you got bidirectional threads (pattern looks the same if you flip tire 180, see sidewall for rotation direction mark) then you have nothing to worry about, these tires can be installed both ways.