Do you have any brands in mind? In the bagged tea with cellulose tea bags that I've bought, they are typically held together by just a staple. I've found this to be the case since I occasionally empty the tea from the teabags into my percolator.
Edit: Also some tea bags for loose leaf tea like t-sac or finum brands have that crimp on the edge. However, t-sac confirms they use glue, but finum specifically claims to not use glues, so maybe it is jumping to conclusions that all bags of these sort do.
They've since reformulated the bags - can't find any statement about the new flat bags.