Can stock rod and stock crankshaft handle the power?

I've had muscle cars most my life and my 410 stroker is the first true 425 horsepower car I've had. There's a large jump from 400 to 500hp . My duster with street tires only holds traction til 1/3 throttle in all 4 gears. I also have 410 gears, 28/10.50's Hoosier's for the track. I get full traction by third on a very - very well prepared track.
What my point is and not to be presumptuous, have you driven a 500 or 700 horsepower car on the street or on the track? I would highly recommend going with motor only for a few test hits if you're not completely use so that kind of power, because it will be quite surprising to say the least especially when you put slicks on it.
I have a friend who has a 74 duster with a true dyno'ed 506 horsepower to the wheels ( probably 625 at the flywheel) and he does 10.2 @ 135. 700 horsepower would be well in to the nines and possibly into the 8 second quarter mile and at that point I hope you have a lot of stuff certified..