skychaser30 and gorz's answer should be ignored. Whether or not your CPU will bottle-neck two GTX 580s will depend on several other factors. The games that you play, what settings that you play at, and to what degree background tasks are impacting your performance (especially if you're multi-tasking while you game). Anyone who says yes or no to your question without asking you exactly what games you want to play and how you want to play them is giving an inaccurate answer.
EDIT: Also, for gorz, any FX-81xx CPU with the second core of each module disabled and the CPU/NB frequency brought up to 2.8GHz or so can compete with even the multiplier-unlocked LGA 155 i5s in OC versus OC performance comparisons and can compete fairly well in power efficiency against the i5-2500K (the 3570K has it beat pretty significantly in that). Knowing how to use an AMD CPU properly can give you a very surprising powerful computer.
It's not as simple as using Intel's CPUs (obviously a strike against AMD, but regardless) and when you see them compared on similarly simple setups such as not going beyond multiplier and/or base clock frequency overclocking with or without overvoltage is wasting a lot of potential on AMD's CPUs. They can be optimized in more ways than Intel for similarly incredible performance to Intel with excellent power efficiency too. Not many sites go the extra mile and review them properly, so it's not a surprise that you might not be aware of it, but now you are.