No it isn't- currently it is impossible to connect to other consoles using a different console/PC with any game. Even if it was, it wouldn't be possible to connect to last gen with next gen, so it will never be possible for the PS4 to connect to the xbox 360. It MIGHT be possible in like 7 years or so to connect the ps4 to the xbone, or the ps5 to the xbox something.
TL;DR: No you cannot.