If there's money to be made, yes I think hardware partners would try. However, can they compete with MS and Sony on hardware with commodity PC components stuck together, and the need for the profit margins that MS and Sony can do without?
In a first time (/first gen product) I think no, I'm not sure what is their best chance to gain traction (early on):
High end and expensive though not different than windows PC which are set to remoin for a long while both forward and backward compatible
Low end: could be kaveri+4GDDR5 solder to board, an HDD slot, or a matching Nvidia solution if their custom CPU made CPUs is ready sometime in 2014.
I think that there is no middle ground for them. Sony and MSFT are already here. I would favor the low-end approach, making Steam OS based on SOC only. ANd I'm cheap but I believe that the masses are too.
On the publisher side, is Linux really a 'growth' market? They have Xbox, PS, ios, windows, mac, android, is there really a need for another platform to grow the gaming market? What gamer will the Linux/Steambox market capture that they isn't already covered on the Ven diagram by one of the others I just mentioned?
Well it is not Linux it is Steam OS, I expect it not to have the same desktop feel even tough, desktop applications could be ported (/recompiled) easily.
Publishers are tough bet, clearly I can see them wanting to break out of the MSFT/Sony duopoly /grasp.
It could get complicated, AMD and Nvidia have working relation with studio, help with development, take in charge a lot of optimizations, etc. On the other end Nvidia and AMD , Intel are on the wrong side of the stick (AMD got all the deal though) if you look at the profits MSFT and Sony plans to make on consoles or MSFT makes on PC, they may think that they don't get a fair share of the revenue they are generating. Actually the same is true for software, both MSFT and Sony just removed ~60 bucks out of the budget of gamers that play online for them selves, it is hard to argue against that from their pov it is a loss.
In the mean time MSFT is mismanaging Windows, the "free approach" of Google and the festering Android environment may have given a couples execs some ideas.
It is not a given but both hardware vendor and software may have seen there best interest in supporting a free environment, not being locked in a duopoly, etc. They could deem the option worth a try it fails.
I would also bet that some people in the industry might think that this gen went wrong, too much of a jump in tech, too brutal, lots of investments, in the end the generation both MSFT were not aggressive in lowering the price of their systems lowering the extend to which editors could recoup their gains. etc. There are a lot of issues that are not there in an open market, tech evolve smoothly, there is competition on price, it could be blood bath with desktop class ARM processor available to lots of integrators. For the software guys, they benefit form the hardware guys optimizing their software for the sake of selling their hardware.
I see lots of reasons for the hardware and software vendors to "try" something different, it fails it fails. But I've the feeling that whereas the start of that adventure could be sluggish it has a potential to snowball as the tech progress (a bit like Android), I go back to your first point the hardware, by 2015 (could read as: as early as)there could be threatening products shipping.
PS I'm not clear at all this post sucks... should have made a proper "plan" before beginning to type