Sadly, this is VERY unlikely I think.
One issue with PC/XBOX cross play is the slow update time for XBOX, updates have to go through the M$ procedures before they roll out. So, PC and XBOX game versions are frequently out of sync, and often for quite a while. This would make stable cross-play very difficult to achieve.
I wonder what the update roll out procedure is for PS4, if there are fewer/no delays then it might be possible to get PC and PS4 cross-play.
Of course, the other issue with cross-play is that development for each platform may not always be in sync, some issues might arise on one platform and not another and so to achieve cross-play you end up having to delay updates on one platform due to issues on another. That said, we have PC and MAC cross play and we have definitely had issues arise on MAC that did not arise on PC, so perhaps this is less of an issue.
The final issue I can think of, off the top of my head, is the disparity in controller hardware (I know the PS4 has at least 1 HOTAS). Gamepad style controllers are no match for Joystick or mouse, so commanders on console platforms would be at a distinct disadvantage to those on PC, in many cases.
I would LOVE to hear from the devs on this point.