I don't think it's allowed, at least with the train operators we travelled with. We made an error in Balloch when getting tickets, and when we got to Dumbarton and tried to get on board without the right tickets, we were very nicely told, "no".

You have to have the bikes booked with tickets to get on, and they are usually checked. on the platform.

I hope you have a great time... and the rain has stopped by the time you get there!