The roach allows the sail to form a curved surface, creating an airfoil, and threrefor generating "lift", just like the wing of an airplane, or the rotor blades of a helicopter.
The Luff and Loach of the sail are equivalent to the leading and trailing edges of an airlplane wing, and the straight lind distance between those is the "chord". (also, the aeronautic equivalent of "roach" is "camber")
The air flowing past the sail has to flow faster on the convex side of the airfoil, which results in lower pressure, which is called "lift". The"lift" is more or less perpendicular to the chord, so of course in the case of the sail as airfoil, the "lift" pulls the sail and boat forward, rather than up.
If you think about sailing on any point higher than a beam reach, you can see that it is the lift generated by airflow over the curved shape of the sail, and not increased sail area that is propelling the boat forward. It could be argued that increased sail area alone is only really advantagous when running downwind, wing and wing.
Does that help?
Sorry to debunk that tired old theory, but sails, like airplanes wings do not work because of our friend Bernoulli. Instead it is the Coanda effect (
) that supplies the "lift" on our boats (and airplanes).
Basically, a fluid attaches to a curved surface and is redirected off that surface providing drive. (simple explanation) Think of what happens when you turn on your kitchen faucet. Now, take a simple tablespoon and hold it vertically w/ the underside of the spoon towards the running water. Slowly move the spoon towards the water. When you actually engage the water what happens? (rhetorical question) The water attaches to the back of the spoon and is redirected out of the flow and sprays out into the sink. That's what happens w/ a foil, be it a wing, a sail or a keel. Subtle difference from Bernoulli. And why a jet fighter that has almost no curvature to its wing can fly upside down. It just has a higher angle of attack and thus forces the air downward. Sorta like what happens when you stick your arm out the window of a moving car w/ you hand held flat. If you tilt your arm so your hand is acting like a wing, it wants to rise.
But, back to the OP question. Roach, as has been pointed out adds more sail area providing more drive. And yes, the further up the mast you can add sail area the better because of surface friction. That's why all the hot race boats have the square top mains; puts more drive at the top of the mast where there is better wind speed and apparent wind angle.