AppleCare+ must be added within 60 days of purchase from Apple or an Authorized seller. And the only source of Apple OEM factory refurbished items is from the online Apple refurb store - Apple OEM factory refurbished products are not sold anywhere else. Those from Apple have a full standard one year warranty and are eligible for AppleCare+.
Any refurbished device from a third party seller was refurbished (and you should check what they actually mean by using that word - often they do very little to nothing) by a third party and only comes with whatever warranty the seller provides. Example: Amazon refurbished iPhones are refurbished by whomever Amazon contracts with and only come with an Amazon warrant (they are also not eligible for AppleCare+).
And also note that Apple does not provide access to their OEM factory parts to anyone but their own Authorized service providers. So third party refurbishers are left to only using used/salvaged parts, knock-off parts, or non-OEM alternative parts.