Having raced modern small bike engined cars and shifter karts and even an A-mod at SCCA autocross (including nationals) I can confirm that no, an FV will not take TTOD at a competitive autocross.
A good judge of performance for cars in the classes is the PAX index for adjusted top times- 1.000 is the fastest recorded times, everything is normalized from that. Every year, either A-mod cars or FSAE cars post the fastest times at nationals. The rest of the top times in each class are normalized.
http://home.comcast.net/~paxrtp/results/nationals/2011_nationals.pdf
PAX for the class most FV cars would be in would be about .900
That doesn't mean it's not damn fun to drive one.