Somehow I doubt it.
Larrabee is more up M$'s alley. Quick, cheap & nasty. The x86 compatibility would help their bottom line, as it'd be quite quick & cheap to adapt current games - just add a new video driver
And in addition, M$ could save dollars because they only need a single processor (or multicore processor), rather than a dedicated video processer, as well as a dedicated CPU. Consolidation = $$$ saved
My bet would be that PS4 would be cell based with either more cells, or multi-core cell CPU's & lots more ram
The Multi-Core Cell, or increased cell-count would retain compatibility with all PS3 titles, and retain all the established programming experience - and would significantly lower costs in comparison to writing an new emulator to run PS3 games on PS4 & start everything from scratch.
That means all PS3 owners would likely sell/give away their current PS3 when they buy their shiny new PS4 ... thereby instantly doubling Sony's Console audience.
And all new developed games could query the system & alter their requirements to suit, rather than producing two distinctly different titles optimised for two entirely different playstation systems.