Yes — OBC candidates can apply and compete in the unreserved (UR) category if they meet the UR age limit and eligibility criteria.
If you take any OBC benefit like age relaxation, you are treated as an OBC candidate for that recruitment.
Competing in the UR category means you must clear the UR cut-off, not the relaxed one.
A valid non-creamy layer certificate is required whenever you claim OBC reservation.
Declare your category carefully in the application form, since it usually cannot be changed later.