It's viable if Ofsted radically changes its procedures and criteria. As noted above, much of it is already ludicrously rigid. It is also very paper-based and tick box orientated. For instance, if they ask whether governors are aware of certain issues, it's not enough to say yes, you need to be able to produce something like minutes of a meeting when they were discussed, or a copy of a briefing paper sent to them - you will then get your Ofsted seal of approval even if the reality is that the governors slept through the meeting. The inspector wants to see a lesson plan and wants to see that the teacher kept to it, and the teacher will get no credit for seizing a totally unexpected opportunity thrown up, say, by something one of the children says, to go off the plan and do something inspirational.
What that means is that if teachers have a possible lightning Ofsted visit hanging over their heads, they will inevitably spend even more time than they do now checking their paperwork to ensure that they can produce everything Ofsted might ask for at a moment's notice. And every minute a teacher takes on paperwork is a minute taken away from teaching or doing things that actually further children's learning.
It seems to me the answer is to have a system where inspectors do indeed turn up unannounced, but where they focus primarily on what is going on in lessons, what they see in workbooks, and discussions with staff, governors (when available) and children. They could perhaps be assigned to particular groups of schools so that they can keep an eye on progress, pick up when things are going downhill, and would certainly detect the sort of problems which arose in Birmingham right at the very start.
Dear me, that sounds very like the system we had in place before the wonders of Ofsted.