But the question was - whether a turbine can just be disconnected or reconnected while at full power.
Yes, it can, but is generally done only in an emergency. Power stations will automatically disconnect if the generator becomes overloaded. This is the cause of cascading power blackouts. If the power grid becomes overloaded, then after one station disconnects, they all start to disconnect, very rapidly.
There is a very big relay on the power station, I am told; I've never seen it. It will disconnect the station. But, I would surmise, that this relay is only for occasional use. Repeated usage would ruin it, and it would need rebuilding. So it couldn't just sit there, tuning on and off, everytime the wind stopped and started.