I would say no because a basic qualification is now very easy to obtain - the ICP takes 12 hours and you answer some (multiple choice) questions and there are accredited distance learning courses out there. It would just seem lazy to me if a nanny had had the opportunity and hadn't done it because they assumed that they knew everything IYSWIM. Althouugh 'standards' in childcare and 'best practice' change all the time so I'd at least want to know that at some point the nanny had been told something correct and it wasn't all potentially harmful old wives tales. It needn't be an NNEB/DCE/NVQ, although those would be the preferred option for me.
I've outlined my reasons for why nannies should have training before but a brief recap:
A nanny with 5 years experience can have 5 years experience working with 5 children aged 2 years old. A nanny with 5 years experience and a qualification may have only worked as a nanny with 5 children aged 2 years old but will have come into contact with, trained to work with, and have a theoretical background knowledge of, children from birth to 8, thereby increasing the likelihood of them spotting a developmental problem/knowing age appropriate activities.
A nanny with a qualification will not have learnt everything through trial and error. Some things, like employer/employee relationships, only come with experience but with an unqualified nanny you never actually know what they haven't directly experienced and therefore haven't learnt. It could be something major.
A nanny with a qualification shows dedication, commitment (possibly more important without the years of experience because if you have 10 years then you're pretty committed) and a certain level of professionalism regarding their chosen career.
A nanny with a qualification is more likely to be able to carry out observations should the need arise (eg. suspected developmental delay/additional needs) which can speed up the process of diagnosis because the data has been gathered.
It worries me that nannies can work without any basic training . I personally don't think unqualified nannies should be insured (the companies are taking one hell of a risk there!) and I don't believe any nanny should be working without insurance. I know others disagree - this is just my opinion - but the training is there, it's not expensive, it's not a massive time commitment, so why not do it?
So on second thoughts I might if the nanny was prepared to do an ICP or equivalent. But it would very much depend on the nanny.