You're right on the Asus board - it's the better option.
I think you'll be ok, but you'll be taking some risk of damage to your components, because there is the chance you could be pushing the 25Amp limit on one of the Rails. Here is how it works. Your PSU supplies 3.3v, 5v, and 12v power. If you look on the label, the most important piece to look at is how it delivers the 12V power. In your case, it will show 4 12 volt power sources, rated at 25A each. Think of it as 4 smaller pipes feeding the water supply to your house, instead of one big one off the street. It may be fine, but if you run all your showers off one of those smaller pipes, and everyone takes a shower at the same time, you're going to overload that water supply, even though the overall system is rated for an adequate supply of water. This is what cheaper PSU brands do to cut costs.
To make it more complicated, the sum of the 4 rails can't exceed the 650Watt rating, so that's 54Amps total. So, you have a max of 25 Amps on each or a max of 54A total.
Here is how I am assuming your PSU breaks down the rails:
1. 24pin ATX Power - Maximum rating could be as high as 22Amps, so that probably has one dedicated 25A rail, maybe two. This will supply motherboard power, fans, plus up to 75W/6.25Amps to each of the PCIe slots.
2. 8 pin CPU power - Your CPU can draw as much as 15Amps with a mild overclock. So that's probably another rail.
3. PCIe - The two 6 pin PCIe connectors are rated at 75W/6.25A each, so that's another 12.5 Amps
4. Peripherals - So here is where it gets a little tricky. We don't know what the 4th rail is dedicated to. It could be the 2nd 4-pins for the CPU power, or a 2nd rail for the main ATX power, or it could be the Peripherals. So, peripherals could be on their own rail or they could be lumped in with the PCIe power.
Worst case, if they're lumped in with the PCIe, you'll have a single rail providing all the power for your 2 GPUs and Disk Drive. Each 670 draws a max of 180W/15Amps, divided among the 3 connectors (PCIe plus 2 6-pin), that's 5 Amps each. Multiply by 4 is 20 Amps required to the 4 6-pin connectors. If you add another 2-3 Amps for the disk drive, then you're about maxing out the 25A available on that rail.
Best case, they have the PCIe connectors each on their own rail, or the peripherals on their own rail, but we really don't know.
Bottom line is it will "probably" work. However, you have some risk. If something goes wrong, best case, you just blow one of the rails, and you get a new PSU. Worst case, you do some serious damage to your brand new equipment.
The other thing is with those Sata power adapters. If you use those, I would get one of those and one of the Molex adapters. The reason is that the power from the Sata adapters runs through much smaller pins than the Molex adapters. Each of those small pins is only rated for 1.5 Amps. So on paper you're ok, but it's not ideal. If you stick with your PSU, do one of each.
Bottom line though is, if you want to play it safe with your new components, I would recommend an upgraded PSU before you do the SLI with the 670s . Or, get on the phone with In Win tech support to get them to indicate how the rails are split get the best configuration for your setup.
What I would recommend as a safer option for PSU would be:
1. Reasonably safe option:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139005 - this has a single 12V rail, and it's on a great promo right now. It only has 2 PCIe connectors, but it has plenty of the Molex connectors, which are better for adapting to the 6-pin PCIe connector.
2. Really safe option:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817182133 . This Rosewill is also on a great Promo. It has a single 12V rails and 4 PCIe connectors. This is really the type of PSU best designed for what you want to do with your rig. If you can afford to upgrade, you really want to get something like this before you do the SLI with those 670s.