It is correct in informal speech, at least, and fairly idiomatic. But you must put emphasis on the second "not" --

"I could not have not noticed ..."

And, of course, without bolding the "not" is likely lost to the reader (though this reader noticed it the very first time through).

It is correct in informal speech, at least, and fairly idiomatic. But you must put emphasis on the second "not" --

"I could not have not noticed ..."

And, of course, in written form the "not" will likely lost to the reader if not bolded (though this reader noticed it the very first time through).