Not if they're authorised
https://locate.apple.com/ (Service).
It's always cheaper to get a 3rd party unauthorised repair done, but there is little guarantee or warranty (Which is why it's cheaper). Going to Apple direct or one of their authorised centres will likely be more expensive, but you have those assurances. The price difference may not be as much as you think either. It's probably worth contacting Apple for a quote, then contacting a 3rd party. See what the prices are and go from there.