I'm pretty sure that Bescot Stadium station doesn't have any ticket gates, so I suspect that you'll be fine in that regard.
Unfortunately, I'm not sure about all the legal stuff regarding entering station platforms without a ticket, etc. But someone more knowledgeable than myself should hopefully be able to assist. It may sound a bit stupid, but I wouldn't want to be responsible for getting you and your son into trouble, should there be such restrictions. It's better to be safe than sorry!