Yes and no. On the one hand, very small punctures can be repaired with a puncture kit or by using a good quality tire sealant (affectionately known as Tire Slime). Any other damage should not be repaired at home, though some garages may offer to repair some tires.
Really though you’ve got to ask yourself if it is worth it. As we’ve shown on this list, cheap motorcycle tires can still be effective, and even those with tight budgets can pick up new replacement tires easily enough. Motorcycle accident rates have fallen in recent years, but it still remains a more dangerous mode of transport than most other kinds. Adding to the risks by not adequately replacing a damaged tire just seems crazy to us.