Very Nice Early Large Cent Needs Unbending

Well, if by "they", they mean "countries, generally", then I suppose this statement is technically true - many countries prior to 1800 did not put dates no their coins, though to be more accurate, I would say "prior to 1600", since by 1600, most European countries had adopted the concept of dating coins.

But if the "they" here is implied to be the United States government, then no. All American coins have dates on them (even if, in certain circumstances, the date appearing on the coin isn't the actual date of strike), even back to the Fugios and Continentals.