BlueRailTrains first board (BlueHorse) did have a 1 amp spec limit, but was able to go somewhat higher. I have several OGauge engines running with this board (track & battery powered) and have not had a failure. However, I would be cautious with G scale due to the typically higher motor current draws. One of the newer BlueRail boards has a 5 amp rating which is better suited to G scale and includes DCC capability.
BTW, my very first battery powered engine project used that same 12V 2000mah NiMH battery and is still running fine today.