If, for instance, you find (and contact) a senior office (the president/ CEO, VP, CFO, CMO, etc) of a company, and send them a networking query, is this a legitimate way of seeking if there are openings in a company? Note: I wouldn't directly ASK for a position (that's not what networking is for) but to address what's going on in the industry as a whole and in their company more specifically. Also, what is the best way to go about doing so without scaring away a potential job offer (or client to perform services for)?
If you know someone well enough to use them as a networking contact into their company, you can just ask them directly what you should do. If it's possible to bypass part of the HR process, they may shepherd that.
If you don't have a genuine relationship with this person (i.e. they would feel comfortable giving you a personal reference), trying to use them as a means to get around HR or any of the normal hiring processes has a high potential to backfire. Most people don't like to have their name dropped by someone to whom they are not close and upon hearing that happen may even go so far as having a negative impact on your hiring possibilities. In other words, nobody likes to be used.
Additionally, I would advise against trying to use high level direct contacts of people you don't actually know. Most executives are busy and on the chance they even see your inquiry, they are not likely to respond positively because they don't actually know you.
If you know them well enough to consider them a personal friend or acquaintance, I'd say go for it.
But be wary of this if you're not absolutely certain you know them well enough. If you wouldn't go out to coffee with them, don't do this.
Furthermore, you have to be careful in how you approach the conversation. Don't just say "Hey I need work." Instead, say something to the effect of "So what's Company X doing in Y field? Anything interesting or exciting?"
Even so, many larger companies have policies in place to prevent higher ups from influencing hiring decisions too heavily - often the best they can do is offer you a good recommendation (Although that in and off itself is still very valuable)
If you're fairly high up in the food chain -- if you're someone well enough known that a company might actually make a position in order to bring you on board even if they weren't hiring otherwise -- coming in from the top can make sense. This is one of the somewhat specialized techniques executive outplacement firms train their clients in.
If you're a student from a top school that that company has a history of preferentially hiring from, this may be worth considering. For example, IBM used to screen MIT recruiting through the research division rather than the normal paths.
If you're looking for your first job right out if school, and again have exceptional grades and/or an exceptional school, the sheer chutzpah of contacting an exec directly -- if done respectfully -- might occasionally work in your favor. I found myself unexpectedly in an interview with CDC's director of research -- turned out he answered his own phone and appreciated the fact that I had made an extra effort to find out exactly how to contact him. (I didn't get an invitation for an on-site interview, though, so arguably that wasn't a success.)
But if you are an ordinary schlub rather than something special, they will probably just hand you right back to HR. Whether they are annoyed or not will, again, depend on exactly how respectful you were of the value of their time, how much they enjoy teaching, their mood on that particular day...
It can be made to work, sometimes, for some people in some situations. But it does risk being a double-or-nothing bet. Cue Dirty Harry: "Do ya feel lucky?"