Maybe. Only one axis works, which suggests a mechanical design, not optical. A mechanical mouse or trackball has two rollers which meter the motion in the X and Y axes. One possibility is a support holding a roller broke so one roller isn't in contact with the ball. Another possibility is the metering mechanism attached to the roller may have been damaged. It's possible that an electrical component became famaged in the fall too, but that's more difficult to detect if you're not familiar with electronic components and how they function.
If you open up the shell you should be able to examine the rollers and meters for damage, but if that turns out to be the problem, I don't know how you'd find just the mechanical parts you need. But first thing's first, pop out the trackball, remove all screws, and carefully open the shell, there may be some plastic clasps or tabs holding some areas inside the shell together.
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