As a linux person, I have to say that it's not likely in a direct sense.
So most Aviation companies will not have the ambition to change their front end, or user side to a conventional Linux distro.
What is more likely is the companies changing to a web based architecture that is OS agnostic.
That said, of you use any Android solution or ChromeOS, it's Linux. 75-95% of mobile devices use Android depending on region.
If you use MAC, it's a UNIX system.
For Aviation tablets, iPads are the de-facto solution thanks for Foreflight who refuses to provide an Android solution and all Android Aviation equivalents have been 'meh' at best.
The internet is basically powered by Linux. (something like 99% of all servers are some form of Linux.
So it comes down to the desktop and laptop computers.
Most companies supply the pilots and mechanics with iPads.
All that is left is a few conventional desktop portals for general use, or personally owned laptops.
The laptops are becoming dominated by Chrome Books unless someone is really dedicated to photo editing and movie editing (then use a MAC) or Gaming (then use WIN10)
I use a Chrome box ($150) with an old 24" monitor for general use, WIN10 for games and sims, and an iPad for work and travel.
The I.T. industry is really going for a browser based experience, so it doesn't really matter what OS you use.