I did that once after reading an article somewhere, it worked but I didn't like it as well as a good set of stones and oil...it's kind of a pain and a little messy. But, after you get the blades true on the file, wet or dry sandpaper will get your blades very sharp if done right.
I found that a piece of glass, or a dead flat surface like a stone counter top was critical to success. Wet the surface so the back of the paper sticks flat, then wet the top before starting on the head. You need to have the sandpaper wet and flat, very important. I had to sharpen by pulling the head backwards (opposite direction of cut), not push forward like on a file or stones (same direction of cut). Like always, light strokes and count the number of strokes per blade.
Even though I like stones better the wet or dry paper if done properly will get them amazingly sharp. If you go down to the very, very fine grits you can get a polished edge very similar to stropping with leather and compound.