If the A/T is engaged then a single push of TOGA gives you 1000/2000 fpm ROC, after they have started to advance a second push gives you full beans.
Not quite, you need to wait until the reduced N1 has been reached before you press the TO/GA button if you want full GA thrust.
From the Boeing 737NG FCOM. (My bolding)
With the second push of either TO/GA switch after A/T reaches reduced go–around thrust:
• the A/T advances to the full go–around N1 limit.