Sure! Why not? (Though there might be other issues if you put 240 volts across a 120v GFCI :D)
Ultimately, you're describing a sort of tap - though no additional overcurrent protection is needed, as you're within the ratings of the conductors all the way.
Or, are you? Any condenser that calls for a maximum 20 amp breaker is also going to allow the use of #14 wire. You're also going to need a disconnect downstream, in addition to the breaker in the panel
