Yes, they'll be fine. I am using a set of Sony CycleEnergy cells in one of my Electron Beam controllers with entirely satisfactory results.
The biggest issue with most NiMH cells is their self-discharge proclivity. That's why I'm using a low-self-discharge type (these are the ones that are usually sold as "pre-charged").
But yes, an AA-size NiMH cell will certainly deliver at least as much current as an AA-size alkaline cell.