It has to be pretty strong if you want to get to the some of the better presets without duplicating frames, which is half the reason anyone does it. Generally an Intel i7 Sandy, Ivy, or Haswell is the best choice, an AMD 8350 or 8320 somewhat behind it. Anything less than that probably isn't worth the effort.
Though you could make an argument for using one of the cheaper Intel Haswells, relying on Quicksync to do all the encoding, since with Haswell the Quicksync quality is actually quite decent. (Cheapest applicable Haswell:
http://www.newegg.com/Product/Product.a ... 6819116945 .)
If you don't want to stream, just capture to disk, you can probably do that without a 2nd PC using Quicksync or NVENC, or just OBS on UltraFast with a really high bitrate.