No, batteries in general aren't 'noisey'. BUT, if you draw too much peak current, the battery voltage will droop too much, and this will cause problems. NiMH are pretty beefy in terms of (low) internal resistance, but you should check the current draw & battery voltage, especially during RF transmission.

Best to do this with an oscilloscope and a current probe to do this. If you don't have access, or funds, for the current probe, put a small value resistor in the Vbatt+ line and the oscilloscopes' voltage probe across the resistor. Size the resistor so you don't get too much drop, but big enough for the scope to give a useful waveform.