It's worth asking.
When I did, they couldn't guarantee to repair my 2013 laptop, but they sent out a parts request to see if they had a replacement part in the warehouse (top case), and they did have one, and they were happy to use the battery replacement price if my battery showed the "service recommended" state, same rule as for newer models.
They don't provide a warranty for repair on such an old machine, because they can't guarantee being able to find another replacement part.
I asked for a price on a screen replacement too and they didn't have a screen, so couldn't do that. The screen is in pretty good shape though.