I never recommend crossfire or SLI before the facts. I haven't seen any comparison charts for HD 7850s in crossfire versus the R9 290, but I can safely say that you will be much better off waiting until the R9 290 non-reference coolers come out to better cool the card.
Why? Crossfire and SLI are only good when you want to make a value-oriented upgrade. For pure performance, you're better off just buying a single-card upgrade. What do I mean? Say, for example, you already have an HD 7850 and you want to buy another one. That's a good point for crossfire, as the price of a 7850 is fairly low and will give you remarkable performance that exceeds even a single card.
I see your rig already uses dual HD 7850s. To tell you the truth, an upgrade might not be all that necessary, although once better coolers come along for the R9 290, I can safely recommend it if you really want the extra performance.
Crossfire configurations add heat output, power consumption, performance inconsistency, driver incompatibility, and microstuttering. If those are issues you feel you can deal with, then by all means, crossfire is right for you. But if you absolutely cannot deal with things like that, the R9 290 is a great upgrade - once, again, OEMs are allowed to put on their own coolers (seriously, that reference cooler is absolute jank).
Notice that nowhere in this post, did I suggest what you should pick. You will easily see a performance upgrade, and you'll probably see the non-reference cooled R9 290s out by January, so the upgrade will be a welcome one. If you're happy with your performance, there is no reason to shell out the money for it. For 1080p, an R9 290 might not even be all that necessary unless you want above 60 FPS (and have a monitor that can display above that). I always recommend a stronger single-card solution over a crossfire/SLI configuration if you don't already have a video card you planned to buy in that setup to begin with.
tl;dr: Yes, you will. But wait until that terrible AMD cooler is replaced.