My understanding is that TOGA is not required. The whole point of runway analysis and the computation of flex thrust is to ensure that the aircraft will still meet all nominal climb requirements, including engine out, the same as it would if the takeoff were actually executed at the flex temperature.
That said, if one has presence of mind to apply TOGA thrust, then so much the better, as you would perform with that much more "comfort room" and, as stated above it would certainly be a good idea in the event of severe structural damage. On at least some (if not all) FADEC equipped aircraft, TOGA or APR is automatically applied once the FADEC detects the single engine schedule.