Yes, its open to anyone - unless there's a sanctioned event and even then there's enough desert for everybody. I imagine it's for safety as you wouldn't want to get nailed by a 32 ford at 200 plus. We had serious thunderstorms over the last few days yet the salt was perfect. Interestingly, the surrounding areas, freeway medians were mud bogged and full of water - for miles. I was concerned my trip would have been in vain. But hell yes, it was great.
To answer your question, yes you can bring any vehicle you want out there (you can't get it 'officially' timed unless it's an event) but you can go as fast and as far as you want. Suggest you get about 2 to 3 miles north of the last part paved road (to avoid the quick stop tourists - they usually don't go very far inland) and use binoculars to scope out for anybody else before you take off.