Can a bunion that's forcing my toes to overlap cause them to cramp up and lock, too?

It is possible.: The big toe is the strongest of the toe, so as it deviates towards the second toe, the metatarsophalangeal joint of that second ray gets weaker and contributes to forming a hammertoe. As the hammertoe is developing, the tendons become imbalances and can work harder with resultant cramping.

Yes: Cramping can also be caused by severe vascular disease. Be sure to have your circulation checked to rule this out. I would recommend gentle stretching of the toes in all directions. There is a condition called morton's neuroma causing cramping. It would be best to be examined by a podiatrist.

It is possible.: The structural deformity may alter the biomechanics of your entire foot. The change in the structure may cause a change in function leading to possible pain.