To a certain extent, yes. Lenders want to understand how you plan to pay back the money you owe. The best way for them to do this is by asking about your employment status and the income you derive from your job (or jobs).
Although there are exceptions, most lenders like to see permanent positions with a minimum tenure of six months. This demonstrates the stability of the income, which is important since car-loan terms can be several years long.
Pay stubs are the easiest way to verify income, but lenders will generally call employers to verify dates of employment, especially for borrowers with a poor or limited credit history.