I don't think so, only because I have seen flat ground planes. My Starduster
were at a sharp angle. Maybe Scott can knows better. I would think the flat or
GP at 90 degrees to the center conductor is fine.

Straight radials would create a 30 ohm antenna.
45 degree droops create about 50 ohms.

There shouldn't be any current flowing down the outside of the
shield with a groundplane, so you won't need a balun,
unlike a dipole that requires equal and opposite phases.
If you try to feed a dipole with coax, the outer shield
becomes part of the antenna system, causing high SWR readings,
(even if the SWR is low), RF interference and degraded performance.