Yes - you can still lodge a partner visa application as an onshore (Subclass 820/801) applicant even if you have overstayed your visa. From the date of a valid lodgement, you will receive a Bridging Visa A, which allows you to remain in Australia lawfully while your application is assessed.
However, because you were unlawful at the time of lodgement, Schedule 3 criteria will apply. Your application must either satisfy those criteria or demonstrate compelling circumstances sufficient to warrant a waiver. This is a higher hurdle than a standard partner visa application, and we strongly recommend getting legal advice before lodging.

