It would be illegal. First, as a running mate, this would be in the general election and they would have to decline federal financing. Much different than declining federal matching funds in the primary (I worked for Forbes in '96, the first time anyone had declined matching funds since Connelly did way back when.) Second, he would be second on a ticket and by virtue of that would only be able to give the legal individual limit to the ticket since it was not just him running.
For what it is worth, Forbes, who back in '96 was worth at least $500 million, would have taken the federal financing in the general, so I doubt that Marky Mark would even consider declining it given his relative pauper status.