I had originally typed more but after re-reading, I don't think you have anything to worry about.
You are only copying the included (asset) file if it does not already exist in the DirInternal folder. Since it should already exist if the user is updating, the file should not be overwritten.
My app stores settings in DirInternal (and also saves a copy on the SD card) and installing updates to my app does not replace the user's settings. Granted, I am not including a settings file in the assets folder, but again, so long as your code only copies that if it does not already exist in the DirInternal folder, then I don't see a problem.
I assume your app "uses" the database stored in File.DirInternal, not the one in the assets folder.