Random in the time sense. You'll get junk on your serial line, depending on the scenario that can matter a lot.
But yes, if someone happens to be using their serial line for some kind of sensitive signaling, then I would agree that choosing a more isolated connector (or just avoiding hotplug) would make sense.
I assume the possibility of spurious Rx state is why FTDI chose to wire Rx to the tip pin of the female TRS connector: It's the last pin to make contact with anything when plugging in, and therefore least likely to be bridged to ground. I suppose the mechanical design of any particular jack would determine whether it's possible at all.