My question is will it work and be beneficial if I try to use my old Geforce 550 Ti 1gb in sync with my new video card? In essence, I know the gtx 680 will meet my needs, but just as a beneficiary, I would like to integrate the 550 in there as well if possible.
Intended purposes: high settings gaming
i-7 3770k 3.5 (have a hyper 212 evo and plan to overclock in near future)
Intel BOXDZ77RE75K LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
2x 8GB Patriot Intel Extreme Master DDR3 1866
No, the only way you could run this setup would be to use the 550Ti as a dedicated PhysX card, wich would probably decrease your overall performance in games.
Nvidia's SLI technology required two of the same GPU's, the two cards you have use different GPU's.
The reason why you might find a decrease in performance while running a dedicated physX card is the 550Ti is quite alot slower than the 680, so slow infact the 680 would have to slow itself down while it waits for the 550Ti to calculate the physics in the image.
You could always plug it in and test the game with just the 680 and then with the dedicated phyX card running and compare the results.
*edit* A 680 on it's own is enough for almost any modern game to run at a very high detail setting, no need to throw in a second.
Having your 550TI as Physx would not decrease your performance, may be the same, or slightly better in physx games, it would be drawing a bit more power though, most people that by physx cards buy 3-5 year old cards to put in physx, your gtx 680 would not slow down to the speed of the 550 ti, that was completely false.
your best option would probably be to either sell, or save the 550 ti for like a htpc or such