Is a cosmic year the same as a leap year?

A cosmic year is 220 million years, the time it takes for the entire Milky Way galaxy to rotate once.

If by a cosmic year you mean a sidereal year, the answer is still no. A sidereal year is the time it takes the Earth to go completely around the sun, which is 365 days, 6 hours, 9 minutes, and 9.54 seconds.

The difference between the calendar year and the sidereal year (approximately 6 hours, or a quarter of a day) is the reason we add a leap day to the calendar every four years. And the leftover amount (the extra 9-plus minutes) is the reason we subtract a leap day from three out of every four century years (years ending in '00', such as 2100).