The question is not whether you can, but whether you should.
People who make things deserve to get paid. If you don't like what they make, fine, don't read it.
If you try and rip other people's content sponsors with a bayesian content classifier they'll be more likely to have subtler 'product placement' style sponsorship to avoid your ad ripper. They may also have things that appear as ads to your rip app that are required to navigate or read the site. However, rather than avoid a technical war, why not consider either going somewhere else or accepting that content you like is made by people who like being compensated for it?
I agree with your basic premise--that people deserve to get paid for providing me with value--but not with the mechanism of ads embedded in content.
A few reasons:
If the creator deserves to get paid, he can put up a pay wall and we can do business or I can go elsewhere. If that basic business model doesn't work, that is a strong hint that something is fundamentally broken about advertising.
Also, you pose it as giving me a choice of going elsewhere. How does that work when given a link on HN or in an email or whatever? On some sites, there's an ad right away and I can click a link to skip the ad, I can click "back," or I can look at the ad if it's interesting. Fine.
But if ads are embedded in content willy-nilly, I am blasted with them before I get to make the choice of whether to read the content. Again, there's something broken about the model if the content producer can't set up a simple gate where I can choose whether to do read their content+ads or go elsewhere.
Finally, ads in content are a deeply broken model. The reason Google is worth a zillion dollars is that ads at the moment of search are hitting me when I'm making a decision and they are providing value, even if they are biased. Ads in most types of content are hitting me when I'm not trying to make a decision.
There are some exceptions, and I'll bet they survive. An ad in StackOverflow for a programming tool that matches the answer to a question might work when I'm trying to solve a problem. If sites like that do a good job of working with ad networks to deliver the right ads, they might survive.
Almost all other content-based ads are going to continue to git shriller and shriller as they try to maximize dwindling attention. The attention is dwindling precisely because they are trying to work around a deeply broken interaction.
I don't think that people who use ad-blockers will hurt profit so much, because people like that are probably geeks and they generally don't pay attention to ads unless they are really interested in their content. So if your audience is geeky, you might want to find another revenue model.
I suspect (OK, I'd like if) someone will release a spamassassin/dspam variant targeted at ads as a proxy, optionally with some distributed Pyzor goodness thrown in.
In an ideal world, it would be open-source and locally-installable, a la Privoxy.
In a slightly-less-than-ideal world, it'll be hosted somewhere "out there". It will probably be wonderful for 6-12 months, then bog down as everyone starts using it, then the site owners will use it to start serving ads themselves. At which point their only hope for any kind of redemption will be if they've called the service some variant on 'samsara': http://en.wikipedia.org/wiki/Saṃsāra
