Using a bike with Trek ABP on a trainer
Almost certainly you will damage that pivot and possibly the suspension action. I've used a trainer with a normal quick release skewer, and it tends to mash up the drive side, even if it's a metal end. Plastic ones get destroyed - that's a lot of weight to be putting through something that isn't designed to be weight bearing in that fashion.

My trainer came with a big chunky metal QR skewer that weighed about twice as much as a normal one, but was designed to fit firmly in the trainer, for this reason, but I suspect from what you've said that won't be compatible with ABP.

Given that your setup is perhaps even more risky than using a normal skewer - damaging a fundamental part of the suspension, rather than a cheap QR skewer - I really wouldn't recommend using that bike with a trainer.

Have you considered rollers instead? They're a bit scary at first, but once you get used to them they're a lot less dull than a trainer, plus they're better for developing a smooth pedalling technique.