I think there's lots of misunderstanding about all this.
Don't let MS's PR approach to this convince you throw out the idea altogether.
It obviously cannot be thought of as some general multiplication of local processing power. It obviously is not 'infinite' - in that even backend processing capability available to a single player's session was infinite, bandwidth would limit update possibilities (though that bottleneck would go away in the case of full game streaming, rather than a hybrid model). The best way to think about it is that it could let you do
some things that you don't need a result for in the next frame, faster than the local machine. And for those bits of processing, the network overhead added on top still might make it worth while. And if the economic cost to the developer to use this per user makes sense.
So that's lots of qualifications. But in some situations all these things might make sense.
As for the OP's question - yes. In building a backend for game streaming they'll have a perfectly suitable backend infrastructure for handling game jobs - in fact more suitable than a generic infrastructure that generally targets web service processing ala Azure (although I fully expect MS to ramp up their inventory of boxes targeting game processing, with good GPUs etc). The software interface to let a dev do this is not a huge deal. I fully expect Sony to offer a number of cloud features to devs as part of PS4's SDK, including at some point or other, remote computation. It's an easy way for Sony to make additional money off the infrastructure they're building.
PhysX enviromental effects could be easily done by the cloud, enhancing graphics in a way that is claimed. They have no influence on gameplay and you would never notice particles like dust hovering around with a 200 ms lag.
Any such effects that involve user interaction might not be suitable if you want a 'local' experience wrt latency. In other words, dust going around that doesn't react to interactions processed locally might be a candidate. And perhaps preferably dust - or whatever - that's a bit away from the player.
I think the BIGGER question, rather than technical feasibility, is actually economic feasibility. Presuming a pub has to pay for resources used by players playing their games, I'm not sure a pub will greenlight the usage that could be regarded as superficial. At least depending on the business model of their game. If you are doing subscriptions or have good recurring revenue from players (e.g. through microtransactions), you might be more willing to allow it. And before someone asks...no, I don't think MS will let pubs use this freely, beyond a certain point at least.