You're running into somewhat uncharted territory with this one. The short answer is yes, you can install a stereo system. The real question is do you want to spend the money?
Running a system in a hybrid is complicated, the current stereo circuit is for the most part completely bypassed. A completely new circuit is installed usually run off of an added battery...the battery of course is still charged by the hybrid drive. This is something you'll have a hard time finding an installer for...most have never attempted it and most don't want to be responsible if they should damage your vehicle. Your best bet is going to be a larger, insured, and heavily established installer...usually located in a larger metropolitan area. It's been done, and the Civic Hybrid just happens to be the most popular.
The vibration question is a toss up. There are many that claim added vibration from a "subtle" system will not have any effect on the Hybrid charging system. Others claim it will slowly diminish the service length of the battery system. My personal opinion is this....heavily insulate the area of bass using professional sound deadener. This will keep the majority of deep "vibrating" bass tones from reaching the battery system.
If you're dedicated to the project you'll get it done, be prepared to spend up to 100% or more than a traditional car owner and be prepared to sign a stack of waivers that clear the installer of any liability.
Hope this helps and good luck!
