Of course.
A folding bike, even half-folded is authorized in the public transports even during peak hours.
In the train, you can put your Ahooga between the seats or under the seats.
However, pay attention that in some trains, especiallt Thalt or Eurostar, you'll be asked to put your bike into a transport cover in order no to disturb the other travellers. All our bags and covers can be found right here.