Actually I think you can, because I have.
It takes about 10 times as long, but it can be done.
You have to start with a fairly coarse paper, but that depends on the knife in question and what kind of finish is currently on it.
When I used to do it this way, it was because I wasn't very proficient at grinding and I wanted sharp grind lines. I was afraid of washing them out by going to far with my machines.
So, I would start with 150 grit, some Cool Tool II or WD-40 as a cutting agent, and a sanding block made from either Dymondwood or hardwood.
For the initial paper, 150, 220, 320, 400 you can use just a hard surface sanding block (dymondwood works really well for this). However, at 600 and on, I used a piece of Dymondwood with a 9/10 oz. leather "face" super-glued on (I still use it for hand-rubbed satin finishes).
Anyway, you have to go to an autoparts store or a home center (or any abrasive supplier) so you can buy some 600, 1200, and 2000 grit wed/dry paper.
Let me add in, using your finger with paper over it won't work. You really need to make some sanding blocks.
Once you get to 2000, you need to use a polishing paste. You can get this at some of the knifemaking supply houses or some tool stores. Apply the paste to a piece of leather and work it over the blade.
This will give you a mirror finish, and a very clean one at that. But I can't really say I recommend it. It is a lot of work, and IMHO, the finish you have at the 1200 grit point is more attractive than a mirror polish anyway. Different strokes...
Just my $0.02
Nick