If driving up Diablo the issue is parking. It's forbidden to park on most of the climb and frankly I would hate seeing cars all along the road. I would suggest driving up North Gate Road up to just below the junction where parking shouldn't be an issue.
Driving up South Gate will be very itchy with so many cyclist and pedestrians around.
I am pretty sure you won't be able to climb past the Junction, I suppose the Juniper and Summit parking lots will be used by support vehicles. Of course it doesn't cost anything to check with the Park Service in advance.