No, I don't think it will. I hate this trend of pretending that our relative freedom on PCs has anything to do with the platform. Our freedom on UEFI Secure Boot PCs was hard fought and could be taken away at Microsoft's whim*. They literally hold the keys.
Remember the drama about whether Linux would be allowed to run under Secure Boot at all? That was last decade's reminder about hardware freedom and it had nothing to do with a new ISA. Thankfully Microsoft graciously decided that all Windows 8 logo hardware should allow users to load their own keys, but there's nothing intrinsic about the PC platform that forced them to make that decision, and nothing forcing them to keep it.
To be honest I don't know if it came to pass or not. I'm still trying to find more info on what the current Windows logo requirements for Secure Boot on x86 actually are.
It's not the instruction set - it's the IBM PC-compatible standard that gave us our golden era of desktop computing. Standard bootloaders, standard ports, standard keyboard layouts. We owe it so much.
The move to ARM will highlight the hardware freedom in a big way.
People are used to ARM being different and are that much more likely to forget open, general purpose computing right along with that "old" x86...
Heh, I always disliked x86. But now? I look at it fondly.
Strange times.
Edit: It is the IBM PC lineage I speak of here, not just the ISA.