This would be an amazing project. You would need some serious sponsors.
I would say the battery tech to make this possible exists with 90C Lipo available from polyquest. There is the potential for gigantic lipo fires but hey.
What I would like to know is if there is a company out there that could make a compact controller/inverter that can take that kind of power. An AC induction motor may be desireable at these power levels as the looses in a brushless DC motor would be significant. Then there is finding a source for a lightweight, water-cooled 700 KW AC induction motor. The biggest I've seen for EV applications is 200KW. Maybe if you cooled that one with liquid nitrogen you could push 700KW through it
As far as batteries go there are some out there that you could arguably use to make a prototype. Polyquest 45C-90C Lipo http://hobbycity.com/hobbyking/store/uh_viewItem.asp?idProduct=10090
Lets look at this battery hypothetically:
Voltage: 22.2v / 6S1P
The max power of one of these batteries at 80C would be:
80C * 4.4Ah = 352A
Voltage would sag a bit we'll use 21.5V * 352A = 7.6 Kw
So the number of these packs you would need to produce 700Kw is:
700/7.6 = 92 Polyquest packs
Weight of Battery = 92 * 0.748 = ~70Kg
The battery would most likely need cooling and a tough box and all the connections and water cooling, so it would probably come out to about 80Kg
The cost of this battery pack would be:
If the retail price of these packs is $242, then the cost of the equivalent number of cells per pack, straight from the polyquest factory should be about $50-$100
The cells and connections between them should cost about $100 per equivalent polyquest pack. So that is 92 * 100 = $9200
We're looking at a $12k-$15k Battery pack.
This Battery would have: 22.2V * 4.4Ah * 92 = 9 KWh approximately
This would be about enough for 45 seconds of run time at max power of 700Kw.
All this is hypothetical of course.
Now lets look at hypothetical performance characteristics.
At 90% efficiency we would have 700*0.9 = 630KW on tap.
To get to 200mph(90m/s) you would need this amount of time:
Estimate the weight of the vehicle + rider at 350kg
0.5 * 350kg * (90m/s)^2 = 1.42 Mega Joules
1.42MJ / 0.63MW = 2.25 seconds
Add a second or two to account for drag and other losses: 4 seconds to reach 200mph!
Theoretical performance characteristics matching the top fuel pros who do over 220mph in a little less than 6.5 seconds!! You may need a fatter rear tire for that future brushless drag bike, seeing the size of the bikes they use to get those times: http://www.youtube.com/watch?v=VKe74wWwteM