The short answer? Probably not.
The long answer has nothing to do with separate networks or anything similar. I mean, if Constantine is showing up in “Arrow” Season 4, then that’s possible. No, I mean that, story-wise, they don’t exist in the same contonuity, or at least timeframe.
Spoilers for “Arrow: Season 2.5”, and possibly some for “The Flash” Season 2 and “Supergirl”.
For those of you who don’t know, “Arrow: Season 2.5” is a 20-issue comic that takes place between “Arrow” seasons 2 and 3. In Chapter 16, “Flames” (released March 30, 2015), when talking to Helena in Iron Heights, Oliver mentions that the only way Hogue could’ve survived the fall from the helicopter was if he was “secretly Superman”, to which Helena replies “What’s a Superman?”.
A section of “Arrow: Season 2.5” chapter 16
While this may reference that Superman exists in this continuity, you have to realize that having an established and public Superman is required for “Supergirl”. This actually makes sense from a timeline of age – in the comics, Oliver Queen is much older than the rest of the Justice League, which he makes a point of bringing up multiple times in “Justice League Unlimited”. However, this means that Supergirl can’t happen yet.
Judging from this dialogue, chances are Oliver knows Superman, or at least of him. He probably started heroing during that time, though pretty small scale. Maybe even back in his Superboy/Smallville days. He and Ollie probably met sometime during Ollie’s time away from home, and we’ll possibly be seeing the Last Son of Krypton in the flashbacks of either “Arrow” season 4 or 5.
But does that mean that no crossover will happen? Not necessarily. There’s one link that may connect the two: “The Flash”.
For those of you who are unaware, The Flash can travel through time. He did this during the mid-season finale in Season 1, and it was a major plot point of the season finale. So, if “Supergirl” takes place in the future of this universe, after Superman is well-established, then she could possibly cross over there.
And, even if it takes place in a different continuity, The Flash can take care of that too. Dimension-hopping will be a major plot point in Season 2.
So is the “Supergirl”/”Arrow”/”Flash” crossover episode possible? Yes, but don’t get your hopes up.