Update: Turns out, this is true. As a Valve developer did reply to a user on the VKx Discord to say "they're probably referring to the ongoing conversation, which is currently stalled by the NDA, yes" which I've now seen myself—thanks for the tip, MartinPL.
Update #2: On Feb 25th Easy Anti-Cheat did finally email back to say "Thank you for contacting us! Our apologies for the delayed response. We are in a process of working with Valve to bring the support for Steam Play. However, there is currently no ETA for this."
Treat this with a pinch of salt since we've been unable to confirm it, Valve and Easy Anti-Cheat are apparently working to get it supported with Steam Play.
I've held off on writing about this, as I have tried to reach the EAC team multiple times and I've also tried speaking to Valve. Neither have replied to me, sadly, but the people over at EAC did reply to one user on Reddit to say this:
Thanks for reaching out!
While Easy Anti-Cheat already supports native Linux games, unfortunately it is not compatible with the Steam Play emulation yet. We are currently working with Valve to bring the support for Steam Play as well. However, at this time we cannot promise a release date.
Our apologies for the inconvenience. Despite the troubles, hope you have a great day!
I'm not entirely sure why neither party decided to reply to my questions on this, it could be that they were trying to keep it hush-hush until they had something to show for it.
It is quite exciting if true though, as getting EAC working in Wine/Steam Play would be massive, as it's the only thing currently holding back multiple titles from working well when played on Linux. With that in mind, it wouldn't be the least bit surprising if they are working on it given how it's going to be essential considering how many multiplayer games use it.
Valve/EAC, if you're reading this don't be afraid to reach out, I don't bite.