All things are possible, but there are, of course, trade offs. Most current bows are cut the way that they are so that the arrow passes nearer to center with some actually cut past center to allow a straight shot.
Many older bows and many / most self bows are nowhere near center cut, so the arrow has to bend around more. No biggie, but it is a bit different.
If you cut a bow to center on both sides, well, you get that picture, so both sides of the cutout have to be less, leaving you with a bow maybe 3/8" proud of center on both sides.
Not bad, just different from what most are used to.
ChuckC