The question if they want too, they'll not only have to design a CPU but an entire eco-system around it.
I personally see ARM becoming a potential player through another vector.
We already have various "open-cloud" alliances that design their own reference servers, network equipment and storage.
As ARM being a relatively easy ISA to license it wouldn't surprise me if the likes of Google and Facebook would license it them selves and then come out with their open server architecture which will include an ARM based CPU.
Facebook has released their ethernet switches and server reference designs a while ago, HP has only recently released OpenSwitch which is opensource OS for networking devices, Intel is also getting into the game with their own echo system "Intel Open Network Platform".
To me this form of market penetration seems to be much likely than a slow attempt to creep into the market and in one form or another is pretty much mandatory current datacenter users to switch to ARM en masse.
Especially considering just how fragmented the ARM market is, there are allot of different ARM ISA's and even more implementations of those ISA's which aren't necessarily directly compatible.
If we take Exynos as an example then the custom ARM cores that Samsung developed caused quite a bit of software compatibility issue which is one of the reasons why Exynos devices aren't that popular in the Android development community. Heck it was even an issue for 1st party Samsung software anything that didn't run in a VM had to be compiled/redeveloped for Exynos which meant that even software like Samsung GearVR didn't work on Exynos devices initially.
Which is precisely why i think that a uniform compatible ISA and design from an investment consortium is required for ARM to work out it's kinks and take on the server market. Anything that was compiled for x86 for the past what 30 years will work on Intel's current CPU lines. Yes newer CPU's with additional features, extended instruction sets and their respective supported compilers will enable you to run you software more efficiently if you want to invest additional development resources, but if we talk about low level programming the same cannot be said for ARM in all cases which is a big issue at least as I see it.
