I’ve heard it lots of times (sometimes just as “sixteen sixteen”) - mostly for years though.
And it seems like Wikipedia agrees:
In American usage, four-digit numbers are often named using multiples of “hundred” and combined with tens and ones: “eleven hundred three”, “twelve hundred twenty-five”, “forty-seven hundred forty-two”, or “ninety-nine hundred ninety-nine”.
I’ve heard it lots of times (sometimes just as “sixteen sixteen”) - mostly for years though.
And it seems like Wikipedia agrees:
https://en.wikipedia.org/wiki/English_numerals)