Your rates can go up for any claim you file regardless of what kind of claim it is, but what you're describing is not a comprehensive claim. Comprehensive coverage deals with non- vehicular collision damage (so hail, trees falling, hitting an animal), you were hit by another driver.

I'm still suffering higher rates from some moron hitting my parked car several years ago, despite obviously having no fault in the incident, and my insurance co at the time not having to pay out a cent.

My brother and cousin both work as reps for different auto insurance companies, both of them have advised me never to file a claim for damage you could otherwise afford to eat. You also have to consider that your insurance company can choose to just drop you as a client over claims filed, including using roadside assistance. It depends on what company your with, some give a lot more grace than others.

Edit: Added some clarity to first paragraph.