Can you get AppleCare for a refurbished MacBook Pro?

Apple Care is not applicable to any refurbished Mac that is not sold by Apple itself -- In fact, some third party sellers don't even carry an Apple warranty package, and offer things like Square Trade. NOW -- I am not knocking SquareTrade, which is a reputable warranty company -- but it will NOT get serviced by Apple if needed.

The only refurbs eligible for Apple Care are those sold through Apple's own website.

I would call Apple with the serial number of that computer to see if it is under warranty and if you can get AppleCare for it. I question if the third party that you are buying from actually have a Apple certified refurbished Mac (I never heard that third party selling Apple certified used computers). If I were you, I would only buy refurbished Macs from Apple directly.

Yes. Refurbished machines bought through the Apple Store come with the standard hardware warranty (one year parts) and are eligible for AppleCare Protection Plans.

Third party refurbs will only come with the warranty offered by the seller.