E6xx Battery Change
Yes you can however the alternator will not charge at the correct rate if a greater or lesser battery is fitted.
Furthermore the consumer load cutout is dependent on the type of battery fitted, this is useful when diagnosing battery drain issues. The battery state for a given time can be interpreted through ISTA/D or DIS in the Power Module query.
If an AGM battery is fitted where there was none then your E65/66 will need to be coded (retrofit) via ISTA/p or SSS.
The short answer is yes the car will function ok if you just change the battery without registering the replacement.
But due an incorrect alternator charge rate from not registering the battery, you may have a battery that will never gain a charge rate of above 68%