Yes you can but it does not make sense
ATP 6-22.1 para 2-30. states: Counseling tied to a specific event should happen as closely to the event occurrence as possible. For performance or professional development counseling, subordinates may need a week or more to prepare or review specific documents and resources, including evaluation support forms or counseling records
Based on the situation you outlined it appears this may be motivated by emotion and or the leader was directed to conduct the counseling by senior leadership.
If the leader does counsel you they cannot backdate the counseling statement for January. Meaning the date you sign the document must be the date you were actually given the document and not the date of the actual incident.