We strongly recommend NOT installing the BEDB into the same SQL instance as production databases. This is due to the extra complexity needed for recovery in event of loss of the SQL instance to some kind of disaster.
Because of this (and the next information is more of a personal opinion based on the above point) I would either always keep the BEDB inside its own instance OR if I had to share an instance would only share with IT systems that would typically rebuild their data content if needed (i.e. HP Insight Manager, WuSS, Live Update Administrator etc) I would definitely not share an instance with departmental or operational production databases that might be used (as examples) by HR, Finance or Sales etc.