I think it depends on what materials and what diameters you were planning on turning.
The point of the back gear is to reduce the spindle speed and increase mechanical advantage. The harder materials like steels, cast iron (and some bronzes too) tend to call for a lower RPM and, if the lathe is rigid enough, can benefit from the increased torque to allow an increased DOC.
If you think you'll only ever be using the higher spindle speeds that are available without using the back gear then I guess the broken tooth won't be a problem, since you won't be engaging that gear.
However, I reckon you don't really want a built in capability of the machine to be unusable if possible so if you can find a replacement gear, or get one made, or even make one yourself, then that would be better.