Assuming your mount is at a slight angle to the axis of the bore, you have a given angular elevation between the bore axis and the scope axis. In order to increase elevation, you need a higher front ring, while the rear ring stays lower. If you increase the height of both rings, then you're moving the scope further from the centerline of the gun, but it remains parallel (to within whatever tolerances you can maintain) to the same axis it had a few mm lower on shorter rings. The increase of, say, a half inch between low and medium or high rings on your average weaver rail means your scope line of sight intersects the path of the bullet a few mm higher, and thus a bit further out for a given powder charge and bullet weight.
While the bullet is always falling downward as it leaves the bore, but your bore is typically inclined relative to the scope and mount, it appears to come up, cross your line of sight, and then fall back down again. IIRC, most rifles of 30-ish caliber are set up so this happens at something like 50 and 100 yards. So, with a higher scope mount you're talking about adding perhaps an inch to your first crossing point and subtracting that same inch from your second crossing point, so when the bullet passes up through your line of sight, it's actually at 49.95 yards, and when it comes back down it's at 100.05 yards. You can change that crossing point even more significantly by switching to heavier or lighter ammunition, or a bullet with a higher or lower ballistic coefficient, so I wouldn't worry about ring height eating up elevation.
Look at an AR-15 in an A1 or A2 configuration - that carry handle is monstrously high off the bore line... AFAIK the only benefit of an M4 or A3 upper (other than the M4 feed ramps) is that the flat top reciever can extend a rail from your eye all the way out along the free float tube to the gas block, so you can put a 2 foot long train of optics out there - scope, IR, thermal, or a red dot with a magnifier on the back end and infrared on the front, etc. etc. etc.
For height, though, you can improve cheek weld and make the gun more comfortable to shoot. The only time a height issue should be considered for accuracy is when you're talking hitting a target over 800 yards away and you've run out of elevation adjustment with your cheapo wal-mart scope. At that point, an elevated rail (again, at an angle) would help quite a bit.
That's just what I've learned from researching my mosin nagant scope mount project, so someone else chime in if I missed the mark.