Dyeing shouldn't affect the waterproofing, but waterproofing may well affect the dyeing. The dye needs to get to the leather/fabric, so any waterproofing (polish, etc) that you've already put on could affect this. Get into the heather a few times to lose the waterproofing and you may stand a chance.
The other feature to consider is the colour of the sole. Unless it's leather, the chances of re-colouring the seen edges are about nil, so unless you've got black soles, I wouldn't waste the effort trying.