I can’t really comment on that, as I have no knowledge of the 777 having never flown it. However that was an attempt to go around initiated after touch down, which isn’t what the OP on this thread was talking about.
But ok, I’ll modify what I said. With speed mode selected pressing TOGA will, if it is working as designed, with the aircraft airborne, give you TOGA thrust. Totally nothing to do with the flight director commands which will happen whatever the A/T is doing.
Of course you should still be covering the thrust levers and do something yourself if they don’t move, same as any time a power change is supposed to happen with the A/T engaged.