So the answer is yes and no. We don't have a direct answer on Greyfax herself, but
GW wrote this in the Genestealer
FAQ for Servo-Skulls, which are very similar:
Q: Do Servo Skulls prevent a unit from using the Cult Ambush special rule within range?
A: Only when that ability is being used before the
game for units using Cult Ambush as they Infiltrate. In
subsequent game turns Servo Skulls will not affect units
using Cult Ambush at all.
Since Servo-Skulls prevent Cult Ambushes in the Deployment phase it's likely Greyfax does too. Once the game actually starts though the Genestealers can return to ambushing normally.