The voltage of the battery will not affect the power of the shot, it affects the Rate Of Fire and Trigger Response (how long it takes from when you pull the trigger to when the gun fires). Basically it's a case of more voltage, the faster the motor spins which gives a higher rate of fire than a lower voltage.
Trigger response is slightly different however. Another thing which affects trigger response is how quickly the battery can deliver full power. For eg a poor quality 9.6V battery may provide a higher ROF than a good 8.4V, but the first shot could be faster if the better battery delivers enough current to spin the motor faster than the crap 9.6V - it's all about the battery chemistry.
To answer your specific question, the difference between 7.2V and 8.4V batteries will not risk causing any damage, because most gearboxes are designed to run on 8.4V or 9.6V. What can cause damage, or simply increase the expected wear and tear so it packs up sooner than designed to, is running gearboxes faster, ie with a higher voltage than they were designed for.
For eg, a good quality AEG which the manufacturer states runs at 8.4V will run fine @9.6V, just faster, however its lifespan will be reduced. If you ran that same gearbox with a 9.9V LiFe, a 10.8V NiMh (although I haven't seen any actually, but in theory you could), or an 11.1V LiPo, then you might well break something - teeth off the gears most likely, but it will definitely wear out noticeably faster.
A poor quality gun (not necessarily just cheap, as some Chinese guns are cheap & good) may well break something in the gearbox simply from running it with one NiMh cell, or 1.2V, extra. This is one reason why people fit upgrade parts to their gearboxes.
Oh yeah, a good make of battery is VP - Vapex.
