I would not recommend pairing a 7850 with a stock Q9450. My old Q6600 at 3.6GHz (which is faster than your CPU at stock clock by quite a bit) would bottleneck even my 5850...it's not "too bad" in games that would use all 4 cores of the CPU, but for any games that use less than 4 cores that are even slightly CPU intensive would see my 5850 get bottlenecked. But as others have side, it probably wouldn't be too bad if it is just single player campaigns for FPS, but for online play, that's a different story...as there are far more explosions, players and open terrain or detailed structures. As for your question would the dip down to 30s or lower be frequent on BF3 multiplayer 64 maps, yes it would be very frequent, as there will ALWAYS be lots of things going on at the same time, unlike single player campaigns where the AI opponents would only be a few of them at a place at one time nor would they spam explosives.
Your best bet for now is probaby try to find a 2nd hand 5850/6850 at around £60. Save the rest of your money and wait till you rebuild your PC before spending big amount on graphic card. Also, what PSU you got at the moment? Cause PSU that comes with a dell machine would most likely not be good enough for any graphic card that require addition 2 PCI-E 6 pin power (or even a single PCI-E 6 pin).