I'm not in favor of a Borg appearance since I'd rather see them do something new, but it would be incredibly easy to justify the Borg showing up within the established framework of the show so far.
They have a ship with an experimental drive system that can take them anywhere in the galaxy in a matter of seconds, so why not have the Discovery jump into the middle of Borg Space during a test and attract the attention of the Collective, which wants to assimilate this new bio-mechanical hybrid drive technology?
The Discovery will have to make their escape by jumping to multiple systems to try and get the Borg off their tail so they can't track them back to Federation space.
Given the already secretive nature of the Discovery's mission, their logs of the Borg encounter are classified and added to the same secret Starfleet Intelligence database that includes the testimony of Zefram Cochrane and Lily Sloane, the encounter between the Borg and the NX-01, the reports of the El-Aurian refugees picked up by the Enterprise-B in 2293, and whatever other information was available that caused the admiralty to dispatch the Hansen's on a surprisingly well-informed mission to track the Borg long before the Enterprise-D first encountered them in
Q-Who?
There's even "proof" of a sort that Starfleet had an established classified Borg Database before then:
http://memory-alpha.wikia.com/wiki/Starfleet_database
Look at the stardate listed. It's the same as the stardate Sulu gives in ST:VI, set in 2293 (but before the El-Aurian arrival and the retirement of the Enterprise-A).
"Stardate 9521.6, Captain's log, USS Excelsior, Hikaru Sulu commanding. After three years, I have concluded my first assignment as master of this vessel, cataloging gaseous planetary anomalies in Beta Quadrant. We're heading home under full impulse power. I'm pleased to report that ship and crew have functioned well."
http://memory-alpha.wikia.com/wiki/Star_Trek_VI:_The_Undiscovered_Country
Starfleet was up to some shenanigans.