I can't find anything to say that it will provide whatever thrust is needed to achieve it. I used to assume that until I read BOAC's post and then I started to look. It seems to me that 1,000 - 2,000 fpm is a pretty wide margin. If somebody said to me that the Boeing engineers figured out a narrow reduced thrust range that would achieve that for all normal conditions then I could accept. Also, it says somewhere that it will maintain pitch until RoC increases and then maintain speed, which also suggests a fixed (or near enough) thrust.
A lot of the answers to these questions can be found in the FCOM, Automatic Flight, Go Around & A/P Go-Around. (In my book it is 4.20.16)