How could he run for the nomination with a running mate?
Officially, he will be a candidate for the Democrat nomination. The Warren thing is pre campaign fodder much like with the Clintons’ “With one vote you get two!” schtick back when. All it really does is to severely limit his options come nomination time should he need a running mate that can actually pull in more electoral votes than Warren’s MA.
If he wins the nomination, he’ll then officially announce she’s his running mate, but he’ll just be acting on what he’d promised early on (if that is the case.)