Calling posted 'available contact' for job at company I really want?

There is 400-500 person company to which I have been aiming to work at for the past 6mo

They always post when they have openings (then take them down) and I have applied to about 4 openings, none of them entry-level/that I was qualified for and never heard back. Finally, they have posted openings for an entry role that I believe I have a solid background/am qualified for. I submitted an app online immediately and am mailing in a hard copy tomorrow. BUT they have a posted 'contact' (HR rep) on their careers page and due to how serious I am about trying to get in here, and with a role I think I am finally qualified for, I'd like to know if I should go ahead and call them as well next week just to vocalize/express interest directly?

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