Yes, but neither of the conductors the GFCI is monitoring is grounded. The neutral in the panel is just for the electronics.
Likewise, for a 120 volt GFCI, it wouldn't care if either of the conductors it is monitoring are grounded or not. The 120 volt model wouldn't care if the electronics were powered by a 110-volt DC battery!
IMHO.
If one of the conductor in the 120v models being monitored wasn't grounded, you wouldn't have a 120v circuit to begin with.
JAP>