This thread seems to be wandering all over the place. Since it seems like the original question has sort of been answered, but clouded with a lot of other info, I'll add my 2¢.
If you are mounting a 1/2 wave UHF antenna on top of a vehicle, with a proper NMO mount, then the roof of the vehicle becomes the ground plane. With a ground plane, the pattern of the antenna is different that if it was floating in free space or simply using the coax shield as part of the other half of the dipole. With the ground plane under the antenna, you'll see about 2.4dBd of gain. Without a ground plane, you'll see 0dBd of gain. The gain is achieved by the change in the radiation pattern of the antenna caused by the ground plane under the antenna. With out the ground plane, you'd pretty much have a dipole antenna with the whip being one half of the dipole and the coax shield being the other half of the dipole.
But I know, you were not asking about gain, but it does show that proper mounting location makes a difference.
As for "grounds", the 1/2 wave antenna does require a ground, but a ground and a ground plane are two different things. The outer shield of the coax will provide the ground back to the radio. If you don't have the antenna mounted over a ground plane, you'd still ideally want a 1/4 wave length of coaxial cable to act as the other half of the dipole antenna, although I've read things that suggest even 0.05 wavelength works. 1/4 seems to be the sweet spot. On UHF frequencies, you'd want about 6 inches. I wouldn't get too hung up on length, though. As was said, the length between the radio and antenna is the "ideal" length, no more, no less. But unless you are mounting the antenna right at the radio, that won't be an issue.
Any issues with the mismatch due to the lack of a ground plane will be worked out when you tune the antenna.
Really, a lot depends on where and how you are going to mount the antenna. I didn't see much in the way of specifics. I've mounted 1/2 wave antennas with no ground plane and less than a 1/2 wavelength of coax between the radio and antenna, and it made the SWR sweep a bit odd, but it worked well enough.