Can you buy health insurance if you have drawn unemployment before?

Yes, as one thing has nothing to do with the other.

Health insurance can be purchased either through a current employer or individually. Factors that the insurer considers in determining if it will issue a policy concern the health of the proposed insured, among others.

Unemployment insurance is not insurance in the same sense. It is a benefit provided by the state in which you live to which your former employer has paid. It is payable to you if you lose your job through no fault of your own, and the duration of benefits is set by law.