I've often wondered about pheromone with marking cages, it seemed a reasonable thing to consider, especially when marking a lot of queens in succession. Lots of things to consider, don't get paint on her eyes or antennae but you can bet that will happen to the next queen when she brushes past a thread with ink on it.
Very rarely do I put a COT over the queen and workers dutifully move out, it's more often the case that they go nowhere and are joined by more bees on top that need clearing in order to even see the queen. Perhaps it is a reaction to pheromone transfer. We once marked twenty queens with numbered discs and used the 'safe' plungers, the bees piled into the plunger and began balling the queen as I released her. My friend uses the one handed type but I think there is a critical point when you trap the queen where you can't see her well enough.