It might be okay. There is not much strain on the back.
Not much different from sitting in a chair and moving your legs.
You could try in a gym on one of those recumbent bike exercise machines. Should be pretty much the same movement.

If you have a normal paddle kayak you have to use your back muscles a lot and move back and forth.
But with the pedal kayak it's quite comfortable. I tend to get lower back aches easily. But haven't had any issues in this regard. Even after hours of pedaling around. If anything you get a bit strain in your knees after a while, especially in the beginning when your body isn't used to this movement.

It's an awesome fishing machine in my opinion. You have your hands free, don't have to buy fuel, can move back and forwards while having your rod in your hand for casting and jigging, hold position without anchoring, move around without getting tired too quickly and at the same time do some healthy exercise.

You can adjust the incline forward or backwards easily with the side strips in the chair.