It seems Trek likes to give the villain a super ship. Nero had one. So, will John Harrison have a super ship like the Narada in Into Darkness?
It is almost certain that the answer is yes:
1) It would continue the trend. Nero had one.
2) The villain having a super ship is "cool" plus it sets up an epic battle with the hero ship, ie the Enterprise.
3) From the trailer, we know that Cumberbatch causes mass havoc on earth and the Enterprise is in a major battle. So, it would make sense that it is causes by a very powerful ship.
Speculation: If Peter Weller's character is some sort of CEO maybe he owns his own starship. Maybe John Harrison acquires one of these starships and upgrades it into a super ship.
John Harrison is a home-grown terrorist, an expert in hand-to-hand combat and psychological warfare. I don't recall many real-life terrorists having technology in advance of the US' best. I suspect he'll steal a Starfleet ship to get from Earth to Qo'nos.
We don't know the Enterprise is in a major battle with another starship, just that it's badly damaged at some point.