This is a weird one.
I only heard the Falcons had interest in Limas Sweed in a report from ProFootballTalk refuting the rumors, which apparently were making the rounds Tuesday night. Sweed is a particularly weird case because he was such a promising pick for the Steelers at one point, but the team has soured on him and he seems to have some nebulous illness/personal issues, potentially serious ones, to work through. He's also known for dropping a (scientific term alert!) crapload of passes, so I can't imagine he'd be real popular in Atlanta even if he did head this way.
It's the nature of this time of year that you'll get bombarded with rumors like this, but the basic idea would seem to have some merit because the Falcons just took a similar gamble on a much more expensive player in Dunta Robinson, who is facing questions about productivity and motivation coming into his time in Atlanta. I wouldn't completely dismiss the possibility of the Falcons picking up a receiver at some point, even if PFT seems to think it's exceedingly unlikely, but the Falcons do seem reasonably happy with their current depth at wide receiver.
If there's an opportunity to get better in some way or another, I do expect the team will take it.