680Ti ? You mean 980Ti surely.
No you wouldn't as its all about bottlenecks. Running a 980Ti with a i3 or i5 processor would be a complete waste of time.
So it sounds like you want to do a new build.
List your existing equipment in full and lets take a look at what can be cannibalised for the new build. e.g. memory, HDs etc.
Whats your PSU?
Yes, meant 980Ti
Here's what I have - not really played games enough to be honest to warrant making any changes in the past few years
CPU: AMD Phenom II X4 965 Black Edition Deneb 3.4GHz
Mobo: ASUS M4A79XTD EVO
RAM: 16GB GSkill Sniper DDR3 1600
GPU: AMD EAH6950/2DI2S/2GD5 2GB 256-Bit GDDR5, 6970 Overclock
PSU: Corsair RM 750
Cooling: Noctua NH-D14, plus 3x 120mm on case
HDDs: Samsung Evo 512GB SSD, 3x WD 2TB Black, 1x WD 2TB
Case: CM Storm Scout. Also have a Lian-Li PC-S80 in the basement that I snagged for $50 on Craigslist