Apparently yeah. In fact, it's actually easy to tell which years are in the 2nd millenium just by knowing its final year.

But people chose to celebrate the new millenium in 2000 because it's much more fun to have every single digit in a calendar year change than having only one digit change and calling it "a new millenium". Also, January 1, 2000 looks and feels so much cooler in my opinion, unless you write it in the dd/mm/yy format (mm/dd/yy wouldn't make much of a difference), in which case 01/01/01 has that nice satisfying feeling of all variables being the same value.