If a person is voluntarily terminated, currently receiving COBRA benefits and takes a new position, is the new employers health insurance provider legally allowed to disqualify the individual for a pre-existing condition?

Yes. The one way around this would be to enroll during the new company's open enrollment period.

This will differ by state in the US, and by policy, Most group plans in the group market allow everyone reqardless of health during the first >>>> days of going to work, or during open enrollment times.

While this is the normal esp in larger companies, in very small companies this may not be the norm.