EDIT: I'm dumb, I missed this part of my power supply description: 53 AMP SINGLE +12V RAIL The dedicated 53A, single +12V rail provides up to 636W power output, ideal for your high-end graphics system.
So looks like I'm good there.
EDIT 2.0: No longer looking at the GT 730. (didn't realize it would be a step in the wrong direction) Looking at this card now, GTX 760 (link is in the comments, SU won't let me post more than 2 links -_- ): Looks like for this one I'll only need a 6pin to 8pin adapter, since I don't have an 8pin native to my power supply.
So I have an older gaming rig that needs an upgrade. Mainly, the GPU from a NVIDIA GTX 560 to a EVGA GeForce GT 730 DirectX 12 04G-P3-2739-KR 4GB 128-Bit DDR3 PCI Express 2.0 Video Card, along with RAM, but that's an easier problem for me to tackle.
My motherboard is this dinosaur: EVGA 120-LF-E650-TR LGA 1156 Intel P55 Micro ATX Intel Motherboard
And my power supply is this guy: CORSAIR Enthusiast Series TX650 650W ATX12V/EPS12V 80
So, looking at the requirements for the 730:
300W or greater power supply with a minimum of 20 Amp on the +12 volt rail. PCI Express, PCI Express 2.0 or PCI Express 3.0 compliant motherboard with one graphics slot.
Looking at the specs on my motherboard, and what my current card is, it seems to be compliant on the PCI front, and the specs for the power supply mention a single 12v rail, which the card needs, along with '+12V@53A' in the output section, which, if I am reading it correctly, seems to meet the 20amp on the 12 volt rail requirement for the card (Please correct me if I'm wrong here)
Other outputs for the power supply:
+3.3V@25A, +5V@25A, -12V@0.8A, +5VSB@3.0A
So my initial research seems to suggest yes, but I wanted a second opinion from someone smarter than me on this. :)
Yes, I know that in the long run, I'd be better off just upgrading the entire thing, but for reasons beyond the scope of this question, not going that route ATM unless I have to.