Although I have never done a saddle, I have done a lot of other tack, including bridles, reins, and breast collars. If prepared properly and using the right dye, it shouldn't be any different. The dye has never come off my tack, even after getting caught in the rain.
If the person knows what they are doing it should work fine. Going from light to dark will work but dark to light might present a real problem. $50 for the labor + materials is not a bad price, IMO.
Oiling the saddle will never give you the look you are going for.