I think people would still vote straight ticket in this regard. Especially nowadays. I think one exception would honestly be 2016, where enough third-party Never-trumpers may sit out the Pres vote but vote for Tim Kaine and allow him to barely defeat Pence.
I'll go out on a limb and dare to say that McCain/Biden would have won in 2008.
The economy was in shambles and Obama brought in voters who weren't interested in voting as well as created an enthusiasm within the Dem party not seen since at least LBJ. I think that while Palin hurt McCain, Obama would've still pulled it off.