I highly doubt it. They lost a lot of their team recently and even before then they were strapped on man power (and woman power). Not to mention the upkeep would take a lot, since PS4 (from what I remember) has proprietary means to make games run while Xbox One and the like require the new Windows store platform thing, UWP. So that is 2 additional ways in which they’d have to program the game. And, they would need certification from both companies, and Sony is a **** about any game that tries to be cross platform, like Eve (since it would then play with Xbox, PC, etc). Not to mention that if they got the UWP version running it would theoretically allow two alpha instances at once (3 if you include WSL).
If you can get a jail broken console though, you can run steam, and by extension Eve, just don’t expect it to run great 
(or even Linux with the “Linux Launcher”)
TL;DR
Too much work, not enough people, and the platform owners might not be too happy about it