Yes - as long as the existing wiring is in good shape there's no reason it cannot be reused. (The wiring on my 1600 was questionable which is why I ran new wires...)
To reuse the existing wiring:
Connect the old generator ARM wire to the alternator output stud. Also connect together the BAT and GEN wires at the old regulator location. This will take care of the alternator-to-starter solenoid wiring.
Connect the old generator FLD wire to the alternator #1 aux terminal. Then at the old regulator location, connect the FLD wire to the low side of the generator warning light.
Be sure to connect the batteries NEGATIVE ground!
If wired right the generator warning light will burn when you turn the key on before starting the engine. The light should then go out after the engine is running.
Note: You may need to goose the throttle a moment after startup "turn on" the alternator - this is normal.