Hahahhahahaha no. (DAHIKT)
In principle you could dismantle and bag it, at which point it becomes Luggage, and nobody cares. Except that it still weighs the same, and no longer has wheels, so it's basically impossible to carry. To say nothing of any actual luggage you may also have to deal with. If you thoroughly research the working timetable and pick a train that's going to have a nice long dwell time at a consistent platform, it might be possible to dismantle the trike next to the relevant train door and lug it on, but it's the sort of thing that makes the cost and stress of driving seem like a good idea.
Any arguments based on a) common sense or b) disability[1] will get you approximately nowhere. If you're thinking you could wheel it onto the train and then dismantle, it, see (a).
That said, we've had a bit more luck with the local commuter trains (back when they were London Midland), whose cycle provision was "put it where it will fit", during off-peak hours. Not attempted it since barakta went electric-assist though, as you have to remove the battery to lift the trike.
[1] If a non-electric cycle is designed or adapted for use by a disabled person, it becomes a Class I Invalid Carriage - legally equivalent to a manual wheelchair. While this means you can ride it on the pavement, for example, it doesn't help you with trains, because they have dimensional restrictions for wheelchairs that the ICE trike doesn't even vaguely come close to.
