No, I had to do this when I moved to Europe with my non-married fiancee.
Some states can give you a statement saying "This person never has gotten married in our state", but they cannot pull the records of every state. In fact, the state that I was living in could not even do that -- only individual counties could pull records saying "This person did not have a wedding within this county". There are no central records.
When I tried to use that as a record of non-marriage, it was not accepted for the above reasons. My fiancee and I needed to give a signed oath to a notary that we were not married, and take that document to the state's office to be apostilled.