Yes, something like that. Прошёл (один) день - Не прошло ни (одного) дня.
But here we also have another phenomenon: a personal sentence with a subject (день) turns to an impersonal sentence without a subject. You can see it from the verb agreement: день прошёл (masculine), so "день" is the subject and it governs the verb. Дня не прошло (neuter) - since the sentence is impersonal now, the verb takes the neuter form.

Note the difference:
День не прошёл - The day did not pass (i.e. it still continues).
Дня не прошло. - No day passed (There was not even a single day).