Diodes are usually used because they allow current flow in only one direction. Your resistor will allow current flow in both directions, possibly resulting in the resistor getting very hot and killing your power supply. Just where are you planning to put the resistor?
We're getting a little off topic, I suppose. We're no longer exactly about the current sensing resistor--we're talking about an issue with using a wire wound resistor.
The diodes we're talking about link the motor leads to ground and Vc, though I still don't understand quite how it's supposed to work, which would be getting even more off topic. The idea was that they would provide a similar service they do the L298, containing the back emf produced when the inductive load of the wire wound resistor collapses.
This can be gotten around by not using a wire wound resistor, but remember that regardless of how big the resistor is, it does need to be rated for the motor power.