If you do try it, then you need to buy a leather needle, most shops will sell one. If you have a good sewing machine like an Elna, Bernina or Pfaff it might be ok but as the previous post said it could put a strain on it. It is the sharpness of the needle which will make all the difference.
Tried one and broke a succession of needles so gave up for fear of wrecking my machine. Am not sure what type of leather you want to sew but it might be worth trying to locate a local shoe menders to see whether they can help you out. The machines they have are probably more of the "industrial" type and more robust.
Well I have sewn a bag using a leather needle but then I have an Elna and you can even sew quite happily over pins and everything .. but they are pricey !
my father is an upholsterer - it depends on the leather. L:eather on a hand bag will not be as tough as leather used on a sofa. My dad has 2 sewing machine, one for normal material and one for use on leather.