Does the Intel pentium G4600 pair well with these pc parts?

I'm currently using an EGPU setup with a EVGA GTX 1060 3gb version, connected to a lenovo light gaming laptop that had a gt630m. I have the gpu connected with a EXP GDC Beast V8.0 mini pcie connection and a 500w 80+ bronze certified evga power supply. Obviously I'm getting bottle necked by my processor (old intel i7 max 2.9 ghz) and I'm looking to build a cheap rig that will run games like GTA V 50 - 70 fps. And Esport games like cs go over 100. My rig currently runs GTA V at 35 - 45 fps with peaks into the 70s and sometimes dips into the low 30s (online). So MY MAIN question is will a Pentium G4600 pair well with 8 gigs of ddr3 1600 mhz ram, 1 tb hard drive (don't care about boot speeds) and a gtx 1060 3gb, and be able to run games like GTA V at high (some very high and some medium compromises) with 50 - 70 fps?
Note: All in 1920x1080p

No. It's not compatible with DDR3 RAM. You could get an LGA1151 board that supports DDR3, but it will be a Skylake chipset and you will likely have to update the BIOS (which requires a Skylake CPU) before the motherboard can recognize it. You'll need DDR4 instead.