I think it could. There are a number of offences that offend the public conscience, and kidnapping of children would be one. A minimum sentence might well survive section 1.
Similarly, legislation with respect to, say, child pornography or other crimes that attract public disgust might well pass the rigours of the charter. It depends on the extent to which you apply the minimum. Is five years adequate; is it proper; is two more likely?
But I agree with you that kidnapping a child has a good chance of being saved by section 1. Not all minimum sentences will fall because of the concerns over “cruel and unusual”. There are crimes that I think society is prepared to accept as deserving of a minimum sentence.