Would this change anything?
Cheney brought serious credidentials, both in domestic as well as foreign areas (I mean, look at the bloody resume: White House Chief of Staff, Congressman, Minority Whip, Secretary of Defense), as well as s**tload of additional connections. Wolfowitz would be laughed at, with no political experience and being just a former Defense Department official with a rank of Under Secretary.
While I don't think Cheney actually brought votes to the ticket (or cost votes), it gave Bush more respectability.