In all honesty, I doubt it. To be honest, I can't tell you for sure because I haven't done it myself and I don't own skyrim. If someone does own skyrim and is willing to disable all other cores in their system, they might be able to tell you, but even still if they get it to work it is no guarantee because the different architecture and clock speeds of a newer chip.
My suggestion is to save your money and upgrade because even if it does run, it probably won't run well.