Yes, for most high drain electronic applications NiMH batteries are ideal substitutes and you needn't worry about the apparent voltage differences. Even though alkaline batteries are rated at a nominal 1.5 volts, they only deliver 1.5 volts when they are fully charged. As they begin to discharge the voltage of alkaline batteries continuously drops. In fact, over the course of their discharge, alkaline batteries actually average about 1.2 volts. That's very close to the 1.2 volts of a NiMH battery. The main difference is that an alkaline battery starts at 1.5 volts and gradually drops to less than 1.0 volts. NiMH batteries stay at about 1.2 volts for most of their discharge cycle. There are a couple of cases where their actual voltage difference may be important to you. In the case of a device like a radio, where a higher voltage can mean a stronger signal, a fresh alkaline battery may be more desirable - but more expensive - than a rechargeable NiMH battery. This is also true for a ...
If the batteries are of the same type, i.e. both are NiMH or both are Lithium-ion, then you can use a higher capacity (i.e. higher mAh) battery instead of the lower one. The reverse is also true. Using a higher mAh rated battery will allow the device to run longer on a charge. So a camera should take more pictures and a music player can play more songs. Keep in mind that it will take a little longer to charge a higher capacity battery. (Staying with the fuel tank analogy from above, it would also take longer to fill a 20 gallon gas tank than a 12 gallon tank).