There is no central database listing which states will or will not run a warrant check before issuing a driver's license or state ID. Because each state has control over the policies of their own DMV, this list would change frequently, so checking with the DMV in question would be the best policy.
The DMV is a state agency, but not a law enforcement agency. Many states provide a portal for users to check for warrants online, but most do not check in the course of everyday business. On the other hand, drivers whose license has been suspended in another state should expect to run into trouble if they falsify the application to obtain a new one. Whether or not the DMV catches it, the new license will not be valid, and this could lead to arrest during a traffic stop regardless of warrant status.