The battery wouldnt drain any faster- the motor pulls current, the battery doesnt push it. Beyond a certain point ( C rating ) you wouldnt notice any difference in terms of punch because the motor will only pull so much current ( as much as it needs to do what you want it too- acceleration & gearing load wise ), but the lipo may well run cooler as it can provide much more current than it is needed too. Good analogy for that is a fit person working out and a fat person working out; fat person will keel over and die from exhaustion long before the fit person
