They do use a lot of power, but since you would logically use something like capacitors, the only variable would be your rate of fire.
I'm betting that it's just a matter of time before tanks switch to hybrid power sources. The Abrams has turbines that are directly geared to power the treads, and they do a good job of transferring that power. The problem is that the only thing that can really use that raw power is the drivetrain. Not only that, but the turbines need to rev up and down or the hydromatic transmission needs to sump a lot of energy to match the power output with the request from the driver.
The next generation of naval vessels have the same problem and are moving to using constant velocity turbines that are revved up to the optimal speed for efficiency and power output and the electricity generated is used for powering electric motors. They expect to generate something on the order of 10x the amount of electricity that they do right now, and that power will be available for use with directed energy weapons. I think it's safe to assume that within our lifetime, those same types of advances might reach armor too.
There are also potential performance and reliability benefits from this too. Instead of two tracks, you could have four (two to the front, two to the back) and have independant electric drives in each. You make the tank lighter and more damage resistant because you don't have all that transmission and driveline complexity. You have more space for armor, fuel, weapons. Also, if you tank a HEAT round to a track, you can still conceivably escape on three treads. If the same happened with a modern two tread vehicle, it becomes disabled.
Additionally, since you'll probably have banks of capacitors charged for your weapons systems, you might have the option of siphoning that power off to run your motors to get the hell out of dodge if someone took out your powerplant(s). In an Abrams, dead engines can equal dead tanks.
Electric drive systems give you the power to use directed energy weapons (and railguns), potentially increase your speed and reliability, and give you plenty of options that the direct drive systems don't.
There's more to hybrid vehicles then that weiner Civic that tried to cut off Lazs2 and instead crumpled into a handful of aluminum and plastic.