In theory, just swapping out the radio should do the trick. Aside from the vin change needed.
Even the 2014 MyLink I tested has Siri and text messaging enabled. Lacks the guidelines though.
If I am reading the OP correctly though, it sounds like they don't have MyLink already installed but want to switch to it. In which case they'd still need a adapter harness also.
The op has a 13 LTZ, 13 was a partial refresh of the gen (gonna omit the long list of changes and deletions) where MyLink was introduced and made standard from Eco trim level on up. Once you hit LTZ back up camera and auto dim was standard. You either added the safety package, and or Nav package(Can't remember if Poineer made a difference "Sun and Sound") but MyLink was there. 14 they did Siri, messaging, XM notifications and a few other things that the 13 lacked. 13 was like the worst year for MyLink and Cue, actually Cue is still kinda lacking today but not as horrible as what I seen in the ATS. Dynamic Guidance and a cleaner resolution was in the 15 model years MyLink but they "felt identical" to the 14 radio features wise.
In short, the OP has MyLink but the one half a step up from what I had in my car. Dealership wise there was an update to fix some issues like not being able to display pictures in that tab way off in the far left icon screen. Newer radio with vin swap as you said "in theory" may work out since all the other MyLink hardware is there.
