Yes absolutely. Acoustic trauma seems to be the largest cause of hyperacusis along with others, like ototoxic medications, head injury, etc. It's not surprising that around 85% of those with hyperacusis also have tinnitus, both of which were likely caused by noise damage in most cases.
Additionally, I was just reading a statistic that said over 50% of people with pain hyperacusis can attribute it to a single noise exposure that they previously received, so yes noise damage is definitely a primary cause, although how similar the type of damage is is a little difficult to say.
From my understanding (maybe others with more knowledge can chime in), loudness hyperacusis is caused by issues with auditory gain, just like tinnitus, while pain hyperacusis seems to be caused by issues with the Type II nerves and/or middle ear muscles. So I assume Susan Shore's device could have some success with loudness hyperacusis since it's very similar to tinnitus, but I really don't know if it will do anything to help pain hyperacusis.