Well, maybe. F1 cars have a lot of downforce, thus better grip. They also have a large drag.
For example, Pro Stock bikes have a WR of 6.777 seconds (actually, achieved last Friday, by Héctor Arana), I believe
they have 320-330 HP (and just one gear). They weight 615 pounds minimum (for V Twin 160 cu.in) or 279 kg. This means 1.18 hp/kg (or 1180 hp per tonne, as you put it). They reach almost 320 kph and they would beat easily an F1 car for the 4 blocks. Of course, that's nothing compared with Top Fuel bikes: they have well over 1000 HP, more than an F1.
Pro Stock world record last year (by Ed Krawiec)
Top Fuel bike (not NHRA, but European Dragsters). Do... not... blink
A Formula One car reaches 320 kph in over 10 seconds.
Last part of the curve (extreme right) shows Fisico at Melbourne going from 70 to 300 or less in over 10 seconds. I have no idea if that's the straight, but I'd guess so
For comparison, Dani Pedrosa holds the world record in Moto GP with a top speed of 349 kph.
On the other hand, ProStock bikes have wheelie bars and large slicks (larger than MotoGp, which have V shaped tyres, unlike ProStock which are flat).
The times I could get for Moto GP indicate a 0 to 320 kph of 10 seconds also.
I'd guess that if a Formula One car could be optimized for drag racing they would use less wing, beating (perhaps) the Moto GP bike, because they could have better grip (with some tweaking to reduce drag but not that much).
Hard to say.