You can use Nimh cells with a brushless, no problem. I've run some brushless motors from Nimh cells, as have a number of people around here.

Brushless motors don't necessarily draw more current than brushed motors. They are more efficient, and you can generally put more current through a brushless motor with out causing damage than with a brushed motor of the same size (since in a brushed motor the brushes burn out first, while in a brushless, you have to get hot enough to damage the magnets or melt wires). In fact, if you use the same battery and prop, a brushless motor with the same KV will often draw less current than the brushed motor when turning the prop at the same RPM.

However, I don't know if that particular pack will work with any particular motor and prop. You'll want to check to see what kind of current you're pulling with the brushless motor, and what the voltage under load drops to. (watt meter-type devices are great for messing with electrics). I suspect that most brushless motors in the speed-400 range will be fine with 1800nimh cells, but a lot does depend on the particular motor and prop.

At this point you can probably get a lot more info and in greater detail about your planed setup by looking through the electric forums. You might be able to find someone with the same setup you're looking at and get some more specific answers.