'You've no idea' isn't grammatically correct either, it's just less obvious.

You could say 'you have no idea,' or 'you have got no idea' interchangeably.

'You've got no idea' would be a correct contraction.

The reason 'You've no idea' feels correct and 'will you've sex' from the original doesn't is because our brains are trained to sort of skip over, or add in if need be, the existential verbs, like 'is' and 'got.'