Do Serena and nate ever date in the second season of Gossip Girl?

No, Serena and Nate do not date in the second season of Gossip Girl. While they have a brief flirtation and a few close encounters, their relationship is primarily focused on their individual romantic pursuits:

* Serena: She is involved with Dan Humphrey, on and off, throughout the season.

* Nate: He has a complicated relationship with Blair Waldorf, and also dates Vanessa Abrams briefly.

Their relationship is largely driven by the underlying tension and lingering feelings from the previous season, but they never officially become a couple in Season 2.