No, they don't. There doesn't need to be an arbitrage. If you have 10 USDT and I give you 9.90 USD for that...nothing else needs to happen.
But the degree that this is happening pales massively in comparison to the billions that are sat on exchanges and recycled.
Tether would be the first legitimate billion dollar operation where people have to say things like "but you didn't hear it from me".