On 777 it will go into an unrestricted climb, 737 and 777 are pretty similar.
Easiest way is if your given a missed approach, before you press TOGA check the altitude selected. The is very rarely a rush to do a go around. If your above the missed approach altitude (on 777 anyway) so long as your above 1500ft if you deselect approach it will default to V/S and decent to and capture the missed approach altitude. When its level then select TOGA and follow the normal procedure.