As a marketer, would you class SEO as a paid marketing channel despite it being referred to as organic and also non-paid, since there's often a cost involved?

Yes, it's a paid channel, hands down, because you need to invest time (=money) and sometimes cash (backlinks, tools, etc.) in it.

Thanks for A2A!! The term organic traffic means for which you are not paying directly to get visitors. SEO is completely a different thing there. Is it necessary for you to hire a SEO firm to optimize your site? You can do that on your own too, if you are willing to donate that much time and learn new things. Google does not ask you to go ahead and hire a SEO firm. So, I wont say that SEO is a paid marketing channel, you hire a SEO firm only if you are incapable to do it on your own or if you are not willing to donate that much time. SEO is a part of your planning strategy on how you have to garner your visitors. Its not like ads where you have to pay for getting visitors. And thats why visitors from ads are inorganic. Now, talking about all legitimate methods, search engines dont even want you to pay for your SEO. As google is advancing, buying links and stuffing in keywords are losing their importance quickly. Hiring a SEO firm that is not aware of all google updates will only land you in trouble in long run. SEO is supposed to be minor editing made by site owners to just improve their visibility to search engines. Leave the rest to google. If you are doing something good, people will link up to you, and your SERPs will improve automatically. At least thats what I think, and it is based on what I have learned by optimizing my sites.

If we are talking about SEO in a technical sense of the word (content optimization, content submission and sitemap generation, backlink quality check, search rankings track, competitor analysis etc.), then it can be done both with cost involved and on a free basis. You can hire an SEO agency to do the work for you, you can register on an online paid SEO platform to automate all the SEO tasks. And there is another option that can fit your needs and save your money. Web CEO gives an access to its powerful all-in-one http://www.webceo.com/free-online-seo-tools.htm to automate an SEO process and provide reports on a regular basis, pointing to crucial positive or negative changes. Web CEO can help you to put your website on a higher level, earn higher rankings, save from low quality backlinks and find new ones with the help of the Competitor Backlink Spy tool at a cost-free or at a minimum cost involved. These important parts of boring SEO work makes it different from paid marketing and brings more traffic that is targeted, relevant and highly engaging thanks to your audit, analysis, on-page and off-page optimization SEO work.

From a marketers perspective, both paid and SEO have a cost, but from the search engine's perspective only Adwords is considered paid media, because they don't get paid to include sites in their organic listings.