Nope. The Kali Yuga began in 3102 BC so a good 12 years after the Long Count. It’s not a calendar cycle strictly speaking however, although it is sort of the same idea the Mayans were working with. The idea that the world/universe goes through phases and cycles of creation/destruction and the dates computed from astronomical observations.
The Hindu are also a little less optimistic than the Mayans: the Kali Yuga (the “age of immorality” where everything is crap and then there’s Justin Bieber) is supposed to last 432,000 years. And its end is a good thing: when it ends, the world will loop back to Satya Yuga which is utmost perfection: there will be no aging anymore, no need to work, no rich and no poor etc…
And of course, no Justin Bieber. I can’t wait.
If you look at the Wikipedia page for the Long Count calendar, you can see a table that matches up rollovers with dates on the Gregorian calendar. The last one was on September 18, 1618 CE. However, the supposed significance of *this *one is that it’s the end of the 13th b’ak’tun of “this world,” which is mythologically the point at which the “previous world” was destroyed and this one created. However, we have considerable evidence that the world existed prior to August 11, 3114 BCE (proleptic Gregorian), which is the date that the Long Count started.
Today is 12.19.18.8.4 in Long Count Calendar. The rollover in 2012 changes the highest digit to 13. It rolled to 12.XXXX about 394 years ago. When that first digit rolls from 19 to 0 (in 4772 AD), that is the end of a “pictun” cycle which is the one associated with universal destruction/creation.