Anything you do to your hair shaft has no effect, adverse or otherwise, to the hair growing out from your scalp. Therefore, coloring your hair will not affect the amount it grows from the scalp. Do be careful about overprocessing your ends as that could cause you to incur damage to them and force you to have to cut them.
Furthermore, your hair only goes white when your root loses its pigmentation. That only happens when the family genes you have inherited tell it to do so. No other factor will affect the natural hair pigmentation at the root.