No, Season 6 of "24" would have been filmed beginning in late-Summer or early-Autumn of 2006. That's when Roger found out he was being written out of the series.

The writers' strike didn't begin until October of 2007. So it was the season of "24" that aired immediately before the writer's strike. (Season 7 of "24" was the one that the WGA strike interrupted, and they ended up having to air it a year later).