No. Taking Open University courses through UCSB Extension is only possible without being formally admitted to UCSB. As an Open University UCSB Extension student, you only pay courses on a per-unit basis and do not have the same access to UCSB facilities as regular UCSB students.
For general information, please see the article, What is Open University?
For information on registered/non-registered students, please see the article, Can students be both registered UCSB students and Open University students?