Yes, can choose. Eligibility to elect COBRA does not change eligibility for marketplace subsidies, or vice versa. If you are receiving UI benefits, you will also be eligible to enroll in a zero-premium marketplace plan with comprehensive cost sharing subsidies.
As you consider your options, you will want to compare provider networks, cost sharing, covered benefits, and other plan features. Also the COBRA subsidy ends after September 30, 2021. At this time, federal agencies have not announced whether people will have a special enrollment period to enroll in marketplace coverage when the COBRA subsidy ends. This FAQ will be updated as more information becomes available.