Pounding repetitively just wont do the spindle ANY good.
This can seriously damage the spindle, bearings and break the back gears. No matter how it comes off this is a bad situation in any case. There are still options though. Pounding using the back gear can, as you fear break the teeth off it. Most of these back gears are cast iron and while strong dynamically DO NOT take impact force well. You can dismantle the chuck in place leaving only the threaded part on the lathe. Hopefully this chuck does not have an integral threaded mounting plate. Apply heat to the face of this mounting plate, keep it low so as not to transmit heat into the spindle. Many SB lathes have plain babbitt bearings and will melt.
By applying heat this will expand the faceplate and hopefully break it loose from the threads. Another option is to put a long 5 to 6 ft 2x4 in the chuck apply your, Kroil to the chuck, hang a weight on the end of the 2x4 (50 ++ lbs) then just just give it time. The last option and least desirable option, again hoping this is just a plain back is just to machine the back off. If it is not a plain back this will scrap the chuck. But the loss of a chuck is better than ruining gears, spindles or bearings. There are no good options for stuck chuck! ;((
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