This is literally the premise of clandestine agencies, and it’s not a new concept. They’ve been around for 50 years now. This isn’t some bait-and-switch, voters have always known what a clandestine agency is.
I understand that there exists some voters who don’t believe that clandestine agencies should exists. Unfortunately, such voters are in the minority. And unfortunately the majority of Americans find clandestine agencies (and in general, a strong defense) to be “socially useful”.
Again, I am directly refuting that argument. Voters can approve of clandestine agencies if they sign onto the fact that there exists some organs of the government that engage in secret activities unbeknownst to the public. What you are saying would only be correct if at first voters expected to be privy to the activities of the clandestine agencies, and then that happened to change. That has not been the case.
I have provided you an actual poll that asks users "do you approve of these secret agencies (that have always been secret)". When presented with evidence that voters do approve of that, it's a bit of a hack to say that it's literally impossible for voters to approve of it. Not every voter in America is a progressive programmer that subscribes to the EFF's world view.
So no, just being polled highly is not sufficient for something being democratically sanctioned. If you want to know if the People agree with what the CIA does let 100 people read the entire archives uncensored without any further justification and see what you get.
Also, the NSA and CIA are act unconstitutionally and then hide the fact they are doing so from the voters. A fairer way to see if there is actually public support would be to allow a group of 100 people into the CIA/NSA archives and allow them full access to the entirety of the uncensored information, without anyone to justify what they have done beyond what has been recorded.
Otherwise, polling people on what unaccountable agencies do illegally in secret is (figuratively) like asking a North Korean if Kim Jong Un is doing a good job. They just don't have the information to judge.