That is very much not the environment sarracenia purpurea evolved in. I can't imagine it will survive very long. They need a lot of direct light, and they definitely need a winter dormancy period. They do not make great houseplants, at least not for more than a few weeks or months.

Tropical pitcher plants (Nepenthes) do make decent houseplants, although they struggle through the dry indoor Canadian winters here. They do seem to capture a lot of the fungus gnats I've been fighting with lately (I can see dozens and dozens in each pitcher), but not nearly enough to make a noticeable difference.