Well, like most computer hardware questions - it depends.
What resolution will you be running it at (if you are using an LCD, probably its native resolution). What settings do you want to be able to run it at? (i.e. do you care if you have to turn it down to low settings, or do you want it to look great).
I found some graphs of frames per second on various different graphics cards, and it doesn't seem to require much (which is what I expected) - every card they tested gave good results!
TechSpot did an even more comprehensive review of hardware for SCII. Gamespot summarised the article thus:
The good news is that basically any modern graphics card will be able to run the game very smoothly on Medium settings, so even if you're not someone with a water-cooled monster gaming rig, you'll be fine. This isn't the most graphically-intensive game in the world.
But if you're in the market for a new card, want top-notch performance in the game without spending a boatload of cash, it looks like the GeForce GTX 460 is the card for you. It was recently released and can be found for about $200.
I don't know much about the current generation of graphics cards, but the GTX 460 [is available on Scan] starting from £120, which is within your budget. If you want an expert opinion on current hardware I recommend picking up a copy of CustomPC (my sub failed to update when I moved house, otherwise I would check it for you - WH Smiths usually have it). I think AMD are currently favoured over NVidia, but it's probably pretty close as usual.
Lastly - SCII is more intensive on the CPU than GPU, so double check that your CPU is fast enough too.
Actually I think this is a case of the developer / support being "lazy". I say this because the Steam store indicates TFU "supports" the following nVidia chipsets:
NVIDIA GeForce 8600, 8800, 9400, 9500, 9600, 9800, 250, 260, 275, 280, 285, 295
All of which are older that your 470. So, in other words, because your card is newer than their game they don't bother to officially support it. However, it really should still work in this case, even if it's not on the "supported" list.
For comparison, I've a nVidia 460 (a step or two down from your card) and it has played everything I've thrown at it - very new and very old. I'd be inclined to check / update / reinstall the card's drivers and maybe even check / update / reinstall DirectX.
If that doesn't work you're in the realm of something more obscure being the problem - potentially including hardware faults - that will be quite hard to diagnose.
Replacing the graphics card may help, but unless you're going to buy something several generations old to pick up a 200-series card, it's not going to be "supported" by The Force Unleashed, as per the list above.
Best Answer
For most graphics cards, GPU-Z will tell you how much a graphics card is being used, along with a variety of other useful stats.
You can download GPU-Z here.
Load up two copies of GPU-Z, and set one to monitor the second GPU. Switch both to the sensors tab, and tick the box "Continue refreshing this screen while GPU-Z is in the background".
Then load up Battlefield 3 - Set it to be windowed so you can see the GPU-Z sensors, or have the GPU-Z windows on your second monitor.
If the GPU load on both GPUs is a reasonable number, then Battlefield is using both GPUs.
Keep in mind that Windows and other background programs can load your GPUs as well. If the usage is above 10% though, its pretty much guaranteed that Battlefield 3 is using the card.
Since your cards are so powerful, also keep in mind that they might not be used fully all the time, especially if you have VSync turned on.