I have worked in property management for over 10 years and a quick answer to your questions is "no." An income verification is used to show the owner/landlord or management company that the potential tenant has the ability to pay their monthly rent based on how much money they earn each month. Typically, the total gross income of the tenant(s) should be 3 times the monthly rent amount. Income verification is not full proof but a tool for owners/landlords to use in the tenant approval process ensuring that rent will be paid.
Now there are some exceptions. A prospective tenant can get a co-signer on the lease (if allowable by the owner/landlord) that will guarantee that the rent is paid even if the tenant cannot pay it, but the co-signer would have to get a credit/income verification as well. Usually this is designed for college students. If someone is moving to a new city/state and doesn't have pay stubs from their new employer, an offer of employment letter with salary amount listed can be used to show that the new tenant will have a job and working upon move-in and be able to pay rent. This of course would be verified.
I hope this information is useful.