Since Medigap is only a supplemental insurance policy written by private qualified insurance companies, it is supplemental or a possible adjunct to another major insurance policy. That other major insurance policy is Medicare. You can be refused a Medigap Plan if you have not complied with their terms of Medicare Part A and B.
The answer to that question is no. Medicare is a government insurance policy run by The Social Security System. Medigap is a private insurance sponsored plan that wants to sell insurance policies to Social Security recepients who are already covered by Medicare. However, that does not mean that private insurance companies that offer Medicare supplemental plans can sell you a Medigap Plan policy on any kind of plan if you are not already on Medicare Part A and Part B.
Some Social Security recipients already on Medicare are fearful of the deductible that must be met if they are hospitalized. That is the reason that private insurance companies that are qualified providers of adjunct supplemental insurance policies for Medicare offera Medigap Plan. The premiums charged are actually for a private insurance policy that will cover the deductible until it is reached and Medicare begins to take over. The premiums that you pay for a Medigap Plan supplemental insurance policy are for a private insurance to pay your hospital costs until you have met the deductible or out of pocket expenses that Medicare requires before it will pay. Medigap is simply private interprise on the part of private health insurance companies trying to get more customers by assisting Medicare recepients.