Gaaah!! The answer is no.
I called the Yosemite info number, 209-372-0200, and hit 3,5 over and over again until I got a live person. And that is your answer -- No.
Another way to get a permit for the backpackers campground: Get a wilderness permit for LYV. There are a few walk-ins available at 11 AM at the Valley wilderness permit office for the day BEFORE a hike starts. (The line forms early!) ...Now, if you got into the walk-in line, and got a wilderness permit for LYV, then you could spend that night (the night before your wilderness permit hike) in the backpacker campground.
(Last fall, when I was there, there were hikers getting the overnight permit JUST to get a pass to day hike the cables.)
Thinking about it, it seems like you could get a wilderness permit for ANY trailhead, and that would technically get you a free night in your bp campground. But you should call that phone number (and do what I did), and ask if the trail head matters for being allowed to stay in the bp campground. I would think that you could snag some unpopular trailhead wilderness permit, and then get that free pass to the bp campground. If the trail head matters, then ask which ones qualify.
I have driven in the night before, arriving around 11 pm and hibernated in my car in the Trailhead Parking (east of Curry Village), but I am pretty sure that is illegal. If they found you, you get fined and have to vacate the parking lot.
