Yes, eligibility for COBRA does not affect your eligibility for Medicaid or vice versa.  Medicaid also offers premium-free coverage (in some states Medicaid charges a nominal monthly premium for some adults) with no or nominal cost sharing. 

As you consider options, you will want to compare provider networks, cost sharing, covered benefits, other plan features.

If you elect COBRA, remember the subsidy ends no later than September 30, 2021.  If income remains at or below Medicaid eligibility levels at that point, you will also be able to sign up for Medicaid then; Medicaid is open year-round for enrollment.