If I understand correctly, you’re asking if someone follows up after sending a resume/application is appealing, not following up after an interview, right?
I’m a hiring manager at a professional services firm. I JUST hired someone who submitted an application online, never heard back from our HR department, and checked our website to see if she could find someone at the local office to discuss the position with. First of all, if she hadn’t made that contact, we probably never would have interviewed her – because we interview referrals first and we had a ton of them. Secondly, it REALLY set her apart in my mind, because our company is one where you have to be very proactive, go ask for what you need/want, and come up with creative ways to get what you need accomplished.
To some companies, I think it would annoy them. But to me, it is AWESOME (as long as it is done respectfully of the person’s time and gives a really good impression of you). The reality is you have no way of knowing which the company you’ve applied to is. But if you’re the type of person who likes to follow up, make sure everything is progressing, etc – you probably want to work at a company where that kind of behavior is received well. So if you follow up, and they’re annoyed by it – maybe that wouldn’t have been a good fit for you anyway.
Here’s what I would suggest if you’re going to follow up. Email is best, if you can do the research and find out who to contact. If you can find out the actual hiring manager, rather than HR, many times that will get you further. Some people/companies don’t like their processes being circumvented, but again – for the type of company I work at, it shows a TON of promise.
I’d suggest a very short email or phone call. One sentence explaining why you are so excited/interested in their company/that position (make it VERY personal to their company), one sentence stating a stand-out qualification that should make them want to contact you, and VERY clearly stating contact information/what you’d ask that they do next.
I’m in a sales-focused organization (although the positions I manage are marketing, not sales), and that is very well-received here. But at some organizations, they are very stuffy/strict about their processes being followed, so you just have to do what feels right to you and trust that your behavior will help you find a company that values people like you. Does that make sense?