Yes, very, very easily.
To put it into perspective, I'm running LoL on a 2010 laptop with a 2.00 GHz processor, 360GB HDD Radeon 4800 and 4GB RAM with no problems. LoL is very low-demand.
It's not really possible to promise no issue no matter how good a machine is built. This looks like you should be able to run the game just fine though.
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