@jamzzy to add an annecdote to @mowens sentiments, my husband’s been applying to jobs, and most applications have been submitted via the internet. He too followed the “follow-up” tenet, but has stopped, because each time, their response has been a curt “We’ll call you.”
In another example, his cousin applied to a position, called the company, and while they were a little friendlier, he was still informed that there were 1000 other applicants for the position in question.
Processing is an apt and disheartening description. It’s so much easier for them to completely dismiss you if they never interact.
I feel that calling after applying in these situations is an outdated practice. You can do it, but steel yourself before doing so.
Good luck!