Can an NDA require you to not only not tell anyone about your signing of it, but also to obscure any implication of your having signed it?

For example, from these comments from this question:

"The NDA will let you know whether you're allowed to disclose that you've signed it or not." – Lilienthal 9 hours ago

Without context, "The NDA will let you know..." is rather amusing. "Did you sign an NDA with company A?", "I am unable to discuss that" "How about company B?" "No" – DoubleDouble 7 hours ago

In this case, could the NDA of company A, be worded so that you'd also have to answer "I am unable to discuss that" for "How about company B?"?

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