DateOverlapsQ
DateOverlapsQ[date1, date2] returns True if the calendar dates date1 and date2 overlap, and False otherwise.
Examples
Check if two date ranges overlap:
DateOverlapsQ[DateInterval[{{2020, 1}, {2020, 6}}], DateInterval[{{2020, 4}, {2020, 12}}]]
(* True *)Please visit the official Wolfram Language Reference for more details.