No, Comprehensive coverage under your auto insurance policy would not pay for your car to be repaired for reasons such as a faulty sensor or blown head gasket if the reason they need repaired are not related to an incident that is considered a covered loss.
Comprehensive coverage covers your vehicle for losses resulting from incidents other than collision. For example, Comprehensive insurance covers damage to your car if it is stolen; or damaged by flood, fire, or animals. It pays to fix your vehicle less the deductible you choose. So Comprehensive does cover you for some non-collision incidents but not the type of mechanical failures you are asking about.
Other than collision issues such as mechanical breakdowns, a blown engine, flat tire, leaky sunroof, a faulty sensor, the need of a new muffler due to wear and tear, etc are not covered since they are not the result of a covered loss under the terms of a car insurance policy.
If the issue with a vehicle was due to an accident that was covered however it would be repaired under the terms of your policy. For instance your radiator getting a leak on its own would not be covered by insurance however if you ran into a deer and that pushed the front of your car in causing your radiator damage than it would be covered under Comprehensive coverage.
If you have a factory warranty, extended warranty, mechanical breakdown insurance or something of this nature covering your car than you could try to use it or make a claim against it for a faulty sensor or blown head gasket to see if it would be covered. You can also check to see if there has been a recall on a part for your vehicle that has gone bad and thus the manufacturer would than cover the cost for repair or replacement.