If you have a group cover, the company cannot deny you cover. You may not be asked to pay higher premiums based on your health status also.
You may be asked to go through preliminary screenings before being granted cover if it is a new plan. The plan may not cover a pre existing condition. If you are HIPAA eligible, you will be offered some sort of cover even for pre existing conditions. You must have 12 months of health cover, COBRA or otherwise, to be eligible for HIPAA. Also, you must not be eligible for Medicare or Medicaid.