Your "idea" has a name, which is string-walking, and is an accepted way of aiming the bow. There is a good section on string-walking in the DVD, Masters of the Barebow II. People who like this aiming method figure out all the different places they need to hold the string at different distances, so that the arrow point is always point-on to the target.
If you do as you are suggesting, without going into full blown string-walking, two things will happen: your point-on distance with be much less than it was before, and you will have to be very careful to hold the bow vertically, as any deviation from a vertical hold will magnify any aiming errors.
I have always wondered about the effect of string-walking on bow tuning myself, but the effect must not be significant, as it is considered to be one of the most accurate ways of shooting the bow.
I don't happen to like this method, because it introduces some of the complexities back into shooting that I was trying to avoid when I switched from compounds with sights to traditional archery, but there are quite a few people who do like it.