The best answer I can give you is, it depends on which Universe you refer to. Classically, kryptonite was an element formed when Krypton exploded, and that's the sole source of the mineral. So that version of the mineral would affect those Kryptonians.
However! Quoting here from Wikipedia on Superboy Prime "As his reality's Krypton never exploded, there never existed any Kryptonite that affects him..." Which implies therefore that yes, kryptonite would have affected Kryptonians except that the only way for it to be made in such a way as to match their particular makeup is for their planet to have exploded. Folks on Krypton Prime managed to artificially create kryptonite, however, which did affect them. Therefore, yes, there can exist kryptonite which affects Kryptonians even without Krypton exploding, but it takes superpowers/superscience to make it.
As an aside, given how much kryptonite falls to Earth, Larry Niven once calculated that the size of Krypton was about that of Earth's orbit around the Sun.