Yes to both questions it does have a voltage regulator and you will blow it up if you disconnect it. On the plus side if you did disconnect the battery while it was running and destroyed the regulator you can buy a new one for under $40.00. It is item 43 on the parts list link I have included.
Don't disconnect the battery when running. It could blow something in the charging system. What you have is just a plain rectifier. It does not regulate the voltage in the system.
