You might try saying, as part of your email,
"I have already submitted my resume through the official web site but wanted to send you a personal note to express my interest [make it short!] and to attach my CV that details my experience in XYZ important qualifying area, specifically x years in y country/position/company name.
Of course write the sentence better than mine, as mine is totally a run-on...

Can never hurt.

If the organization has over 50 employees they have various EOE compliance requirements. Tracking all applications is going to be part of this. So you will need to apply through the website. That said, I see no issue in sending a copy with a cover note to your contact.

Do both. It never hurts to get resume in front of a hirng manager

Depends. Where I work, all applications must be done through a website and resumes uploaded to the server. We have all been instructed that if we receive a resume from someone we know (can be common where I work) we are to direct them to the website. No resumes or applications will be looked at if they come from anywhere else.

Specifically, if you truly believe you're a perfect fit for the job, good enough to merit an interview and the request is to send it to a generic address, are there downsides (and upsides) to sending it to person that you know would be influential in the higher process, i.e. department head?

Can this be viewed as (the good kind) of ambition? Too strong? Or do what you need to do to rise above the competition.

TIA