Battery registration is definitely a must if you are replacing with different type of battery (AGM, etc) or different amperage.
I'm fairly certain that registration of the battery, even if replaced by same exact type & amperage, is recommended.
The BMW 'semi' intelligent battery charging system takes many variables into account when sending charging current to the battery; such as Condition of battery, Temperature, Load, etc. If your original battery was weak & on it's last legs - the charging program was/is much different than what will be needed with a new fresh/strong battery - hence your new battery will be charged under the old charging program which may lead to troubles.
Gone are the good ole days when the alternator just sent out max amperage it could output @ a given RPM and regulate it thru a Voltage Regulator - now that system is replaced with a 'smart' system that uses computer algorithms. Any time you replace a proven mechanical/electrical way of doing things with a computer controlled system - you're in to much more complication & higher costs.
Registration sort of 'resets' the charging program and introduces the new battery characteristics to the car so that it will charge correctly.
Some say they have replaced batteries & not registered and all was fine - others start having all sorts of electrical gremlins begin to happen, & end up registering the battery to fix the problems. So it's kind of a crap shoot I guess - you may get lucky, you may not...
Battery registration is not such a big deal, especially since there are at least (3) avenues to follow - either free INPA with appropriate cable, or the BavTech Tool, or using free software at this link:
Yes, you will have to lay out some $$ for any (personally I have all 3), but it's still less than what the dealer wants to register just 1X, & if you go the INPA route with coding cable, there are a ton of other little cool things you can code/program the car to do