Really just depends. Size of pulley, shape, material, tolerance all matter. If there is a good way to chuck it up, and it fits on the lathe, shouldn't be too big of a deal. Nobody wants to chance ruining your parts or taking the time to ship it.
If the pulley was less than 6" diameter, I could give it a shot, but you would be running the risk of me trashing it and it costing even more than purchasing it...
Drill is a quick way to cut a rough hole of 'about' a certain size. A reamer cleans up a drilled hole, but won't really make its own hole. The reamer can make a oretty round hole to less than .001, the drill will make a sort-of roundish hole to within .002-.003" of desired dimension. The finish will be better with the reamer. If you get really close with a drill you can use sandpaper taped to a rod chucked in a drill to sneak up on it...