Nah, tea bags are not nearly as aromatic as everything else in your pack, especially if they're sealed for freshness in a ziploc bag. And a cup of strong black tea in the morning is worth the minimal risk anyways. And talk about lightweight...
Try this: a gallon size ziploc bag of water with two teabags inside, laying on a hot rock for a couple hours in the afternoon. Makes excellent sun-tea. I've done it in a nalgene bottle too, but it seems to work better in that ziploc. In the evening, add a nip of your favorite spirit for a pleasant nightcap.
Regards,
Wind-in-Face