If we used several as an interferometer and listened in the right bands, yes. We won't be able to disentagle the cacophony, of course, but we'll see that it's there.
From where I'm sitting in my office, I can hear a crowd cheering at Franklin Field here at Penn, when there's a game going on. That's true even though I can't possibly hear somebody whispering there from two seats away.
Detecting a signal, and resolving a signal are two different issues.
The ability to resolve a signal, such as imaging an extrasolar planet, is proportional to the effective linear dimension (e.g., diameter) of the collecting device. (Do a web search on "Dawes limit" for more details.)
Weak signal detection, on the other hand, depends on the sensitivity of the detector and how much signal you can feed into it. The quantity of signal you can collect is a function of the effective surface area of the "collector," which varies with the SQUARE of the collector's linear dimension, e.g., diameter.
Thus, our ability to detect weak signals improves much faster than our ability to resolve weak signals, as the size of our instruments increase.
That's why it is easier to "detect" a signal from a distant star or planet than it is to "see" distant stars or planets. It is far less demanding.
As always, I defer to the resident FR physics/astronomy factotums if I've mucked up any of the details in my simplified explanantion.