I went to my stealership last night to get a quote for battery replacement on my 2006 330i (2005 manufacture date). It has the old lead acid battery, not the AGM battery. The service technician came out and told me that even though they will register the battery if they do it, he doesn't think there would be a problem if it wasn't registered as it's a lead acid type battery. The AGM batteries need to be registered as they are much more sensitive. Anyways, I ended up just buying the OEM battery from them, $176+tax. they would have charged me $376+tax for them to do the whole thing.
I also asked them if there was any point to upgrading to an AGM battery for better performance/cold cranking ability. He said, not really a big difference and not worth it since if you upgrade to AGM from lead acid, then you'll have to register the battery.