Can I use an Arduino board as a USB encoder?
Some, yes, some no.

The Arduino boards that use the FTDI chip can only talk on RS-232 through the USB, so no.

The Arduino boards that use the MEGA8U2 (eg the Uno), if you are willing to re-flash the U2 with a custom firmware, can communicate with whatever you want.  People have re-flashed them before so they appear to be a MIDI device.  Of course, this then stops you being able to program the Arduino as an Arduino any more.  You could get round that by linking 2 Arduinos together with the RS-232 connections and use one to program the other, or connecting some other RS-232 system to your computer to communicate with the Arduino for programming.

Of course, if you're going as far as writing custom firmware for the U2 you may as well just ditch the rest of the Arduino and just use the U2 by itself.