The authors of the bill definitely want to do that. I think the people voting on it are a lot of times just sort of old and out of touch and have no idea what's what. But, they know about winning elections, and if a ton of people call in, their staff definitely keeps track of that and lets them know.
Honestly, I'm not an expert but my understanding is that the argument for or against that you say doesn't really make a ton of difference. It's just the number of people that called that gets reported to them. But they do report the number and pay attention to that kind of thing.