Is it possible?
Yes, it's absolutely possible.
If so, how ?
You don't need to worry about SharedPreferences as android system automatically retains them on update.
You handle any Room schema changes properly (by Room Migration link), if room schema has not changed, no worries.
Room DB data and SharedPreferences will be retained after installing the updated .apk as long as:
You don’t uninstall the old app,
The applicationId remains the same
Just install the new .apk over the existing one. No special steps needed.