I mean interact is a strong term here. You send 0-140 characters towards them and they get to send 0-140 back. Yes I'm sure sometimes meaningful conversations happen, but I doubt that is the norm.

I get to interact with a rock star if I hang out near the exit door after the concert. I can shout at them and (s)he might say something back. If I'm lucky and it's a cool musician we might be able to have a brief conversation...

As a professional, if I wanted to interact with a leader in my field on a meaningful level I would e-mail, write them, attend a speech by them, etc. etc.