For someone who comes across this later:

"If so, would I connect it to a Schedule C?"

There is no Sched C for the job where the person is an employee being paid under a W2. They are an employee. They would be turning in a business mileage report to their employee to be reimbursed at mileage allowance rates under An Accountable Plan (specifically, google this). That rate includes a depreciation component, already.

If they have another "side hustle" business outside of their employment which results in filing a Sched C as part of the 1040, then only that part of the vehicle use is included in that Sched C. It is compartmentalized into that business function, for using that vehicle as a resource to doing that specific business. In general, since that makes this a shared vehicle across a third function at this point, that is another reason to consider mileage allowance rates for the Sched C, and that means, No, the depreciation is already factored into that rate.