They almost certainly do not. However they do count them (well, maybe the intern counts them, but they are counted). And if the counts get big enough, they do start paying attention.
> And if the counts get big enough, they do start paying attention.
This is a while back, now, but I vaguely remember a Reddit AMA by people working for US federal politicians where they indicated that "big enough" is often as few as two for the right type of correspondence (bespoke letters and / or letters to the editors of voter-relevant newspapers, especially if the politician get specifically called out)
Things may well have changed in the interim, but given how often engagement begins and ends at signing on to a form letter, I wouldn't be surprised if this was still the case today.