It'll just coat. Leather is sealed after its dyed to keep the original color in. As far as I know, there's nothing you can use that will permanently dye finished leather...I was wondering the same thing about a brown saddle I got years ago :P
I regularly dye light oil tack to match a burgundy saddle I have (one of my saddles).
I start with a leather stripper. It is really an alcohol base product made to prepare leather to accept dye. The dye I prefer is made by Kelly and I get it at a shoe repair shop. I use two coats then let it sit for an hour. I then use a clean cotton rag to remove any excess and oil it up. I've had no problem with the dye coming off in my hands.
Warning: this is my personal experience and although I've done this many many times I can't tell you what your experience may be. I start out with a very good leather product and take care to strip it properly before applying the dye. I've done this with new and well used reins, saddlebags, and headstalls.