I think you'll find your lens' center performance will be very similar to what you've come to expect on your D300. The D800's pixels aren't all that much smaller after all. I think the people mainly raising this concern are moving from D700 or D3(s) which has much larger pixels than either of these cameras. Corner performance is a different story, however if auto racing is your main subject, I'm guessing corner performance isn't critical to you.
>Do I really need more reach?
If you shoot your 80-200 at 200mm on your D300, then you can do the same in DX crop mode on a D800 and get a 15.4MP image that likely exceeds your D300's image quality, and will probably be similar to shooting with a D7000. However, I guess you're not spending $3000 on a new body to achieve similar performance to what you already have, or could have by buying a $1000 D7000. If you want to take advantage of all the D800's 36MP, then you will need a 300mm lens for that situation (and if speed is important, it will need to be a 300mm f/2.8). If you do a large amount of your shooting at 200mm, then this is something you should consider seriously.
Since you're shooting fast-moving action, it's also worth noting that you'll need the D800's battery grip with AA or the D4 battery, and run in DX crop mode, to match the D300's 6fps.
For me this all raises the question, what do you hope to gain with the D800? This camera is IMO not a state-of-the-art action camera due to it's low-ish frame rate. For what I shoot, I plan to use the D800 for high-res subjects (landscapes) and keep my D300s for high-speed telephoto subjects (birds in flight). You may be better served waiting for a D400, or buy a D700 and use the money you save to buy a 300 f/2.8 lens.