No the F1 cars use an SMG (it may be a multiplate clutch though, not unlike a lot of motorcycles - I've got a recent F1 tech book around here somewhere that'll tell me what type clutch it uses).
Bear this in mind when thinking about a DCT - it has two clutches each attached to a separate shaft (they are concentric however) - one shaft contains the odd-numbered gears, the other the even. It pre-selects the next gear based on observed conditions (throttle position, brake, steering angle und so weiter). That's one of the reasons the shifts are so quick. (Now for those truly interested,
pre-selector gearboxes date back to WW I - the Cotal, nee Wilson pre-selector gearbox was first used in tanks then in some pretty special French cars.)
An SMG is a single shaft input gearbox. It is sequentially shifted which means to get to sixth from third you have to go through fourth and fifth - you have to row all the way up and all the way down that's why you hear the multiple blips whilst an F1/Indy car corners, and why you sometimes hear one MASSIVE blip when a 'regular' manual tranny (which can go from sixth to second skipping fifth, fourth, and third) racing car is under braking for a corner.
Now, if that doesn't confuse the hell out of you, let's talk about derivatives and the banking crisis. ; -)