Tillandsia can work, a lot of dart frog people use them in their vivs. They do need to dry out regularly so can't be kept in a constantly humid section and definitely not wrapped in sphagnum. They're also high light lovers.
I think they could work well in the homes of gentle arboreal species - definitely not the homes of high-density webbers like GBB.
Tillandsia have some specific care requirements. They like bright, indirect light. They need excellent air circulation. And they need to be soaked in water for about an hour twice a week. (You can read more specific instructions online.) Because of this, they shouldn't be placed in terrariums/vivs where they will be choked with webbing. Because you'll need to take them out twice a week to water, they shouldn't be placed in the enclosure of a very aggressive species.
Based on this, I think they would be a good choice high in the tank of a Psalmopoeus sp. My psalmos tend to make floor-based dirt tunnels and curtains and don't web the tops of enclosures. A cork round with air plants on the outside would be a great tarantula + air plant harmony, I think.
Tilandsia should work perfectly granted the T specie is not a heavy webber. They need indirect sunlight, so a lit room during the day will suffice (a badly-lit room will be as dark as movie theater, but you get the point, they just need the regular "brightness, NOT sunlight). Just punch holes on the enclosure for more ventilation. Do not cover their roots with moss either as they have a tendency to rot, just tie them to a piece of wood using a fishing line or whatever, even glue gun works. Their root needs to be exposed for drying. And dont plant them directly on the substrate, you either stick them on driftwood or heck even on the tank wall. Light misting is perfect - they are not a moisture-loving plant and only need water as a need as all living things do. If the leaves are not given a chance to dry they drown. Theyre really easy to grow, some even just hang them, hence the name Air plant because they thrive even via wire-hanging without having to send forth roots.