Would i5-6600 be able to handle 2x RX480?

Dunno.
Depends on the game and your resolution.
RX480 performance numbers are not out yet.

With a budget for those parts, I would look at a i5-6600K and plan to overclock.
Today, there is nothing better for gaming.

And... I would not plan on dual cards initially when a single strong card like a 1070 at 1440P 0r 1080 at 4k will do the job.
Why look for trouble such as screen tearing, stuttering and possibly non support .
 

Alexlomm

Commendable
May 18, 2016
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The target resolution is 1080p. I plan on buying one RX 480 and, possibly, another one down the road(not in the nearest future).

It is most likely, that I'll settle for i5-6600 and one RX 480. Because of this, I would rather opt for non-k CPU. Nevertheless, I'm interested, if I decided to go for another RX 480 in the future, would the i5-6600 be able to handle both GPUs without bottlenecking them? I do realize, that the numbers aren't out there yet, but the result can still be estimated I guess.