Peter, you were lucky they could find sprockets for you. Did they custom drill the mounting holes? What BMW were you riding (F650?)

If you learn about good chains and sprockets then this could save some heartache down the road. Unless you plan a continuous, non stop ride of more than 20,000 miles where you would never see a BMW dealer ... then I would NOT carry a spare chain. Just no need.

Start with the BEST CHAIN: top of the line ZVM DID X ring chain. good for at least 20,000 miles if not more. (I've done 25K miles)

Quality sprockets are a debate point. My experience says OEM ones are best, but not sure this applies to BMW ... as they've a poor rep for using really crap chains and sprockets from the factory.

Japanese OEM sprockets are THE BEST IN THE WORLD.

But, in a pinch, go with Thai made JT sprockets. Quite good, last about 15% less than OEM in my experience but suitable. The trick to getting a chain to last is to swap out the front sprocket before you think it needs swapping.
Like at 8K to 10K miles. IT WORKS!!!

A rear sprocket "should" last 20K miles if a quality item, but lots depends on use and conditions here. Lots of rain or mud is TOUGH on drive line components.

So I would not be opposed to bringing a spare rear sprocket along ... but a PITA to carry. I carry 2 front sprocket with me and always start with NEW or near new chain and sprockets. NOTE: by swapping front sprockets frequently you not only extend chain life, but rear sprocket life as well! WIN WIN!

I've gone 22K to 25K miles on my DID chains using the above technique, staying on the same rear sprocket, riding my DR650 (now at 60K miles). Similar results on former DL1000 Vstrom, 90K miles, got 20K or so out of each DID X ring chain. (stock O ring only 12K miles)

Get the very best, toughest chain you can afford and you will have ZERO drive line problems. Don't cheap out on sprockets. I've tried many different brands over the years and 50 bikes. No name crap sprockets will burn you for sure.
been there, seen it.