The Han calender and all that followed in its tracks in the imperial era were absolutely utilized, at the very least at the imperial level. It was vitally important to the putative success of every reign era (sometimes emperors had several reign eras) that a calender was drawn up at the start, presumably with the most perfect calculations. The true (read: imperial) calender provided emperors with a cosmological constant within which they could govern perfectly. Wrong/poor calender = failed rule.
So, was it used at lower levels? it seems very unlikely that the answer is no, particularly after 1000 ce, when literacy was on the rise. Non religious Scholarship and learning was almost entirely focused on imperial career opportunities, so knowledge of, and adherence to the calender would have been vitally important. All biographies and histories back this up, with calender dates listed liberally.