In storage, batteries will self-discharge over time because of their own internal resistance but if you connect a load across them - even a low current one like a DVM - then they will discharge a lot faster.
NiCAD and NiMH batteries have a high voltage when first charged - up to 1.5v when new. This drops quickly down to their nominal voltage (1.2v) and remains there until they are over 90% discharged, then the voltage drops very rapidly. For NiMH cells the absolute minimum voltage should be 1.0v/cell. Unless you check them very regularly you run the risk of them going below this and into deep discharge, which can damage cells fatally. Unfortunately connecting a DVM across a cell will give no indication of how far along the V/T curve the discharge has gone i.e. how much charge remains. I wouldn't do it, but that's only my opinion.
When in use, however, you will be taking a significant amount of power from them and so the addition of a DVM will make very little difference to the rate of discharge e.g. the voltmeter/battery state indicator on the front of a transmitter.
DM