Flaps One
No I don't think so. If in ALT mode we could still be using managed speed.
Everyone I ask seems to think that the FMGS will give 'Green Dot' whenever there is an engine failure, but as FCOM 4 describes this is far from the case! The a/c might begin to drift back to GD even with the EO CRZ SPD showing on the PFD since there is unlikely to be enough thrust at altitude, but of course that was not the question!
If the a/c is in ALT mode (or actually in V/S zero as we would be the case when accelerating at EO ACCEL ALT) the FMGS will take into account any speed constraint ahead if still using managed NAV. In this way when very heavy, for instance, we might never get to GD (this dependant on if we are still in FLX/MCT not TOGA!).