Only if you buy comprehensive and collision coverage on it. The filing relates to liability, which pays for harm you cause to others. Damage to your own vehicle is separate coverage you choose or a lender requires.
More detail
The state minimum is a liability minimum. It exists to protect other people from you, not to protect your property, and a policy written at exactly the minimum pays nothing toward your own vehicle after an at-fault accident. That is a deliberate design choice by the state, not an oversight. Whether to add physical damage coverage is an economic decision: on an older vehicle worth a couple thousand dollars, the premium may exceed any plausible payout, while on a financed vehicle the lender removes the choice entirely. One related point worth raising with a producer: the state minimum is a floor, not a recommendation. Nebraska medical and vehicle costs can exceed minimum limits quickly, and higher liability limits are often cheaper than drivers expect.