Yeah I wouldn't call that SA. A dog with actual SA basically has a panic attack when you leave, and they do all kinds of stuff they wouldn't normally do, in a blind panic. A puppy that cries a little and chews stuff is just a puppy. My year-old dog chews stuff while I'm right there in the same room!
How are dog reacts to boarding really depends on the dog. My first dog got so anxious that she wouldn't eat while in boarding, so we'd get her back as a skinny nervous wreck. My previous dogs loved going to boarding because they got to bark all they wanted. I haven't boarded my current dogs yet so I don't know how they'd react. But, yeah, totally an individual thing. If she likes the trainer she might actually have fun while you're gone.