Webpromoters,
First, it would help to provide a bit more info as it is difficult to answer a question wherein the only subject source is ... 'it'.
Next, there is no such thing as "no SEO." Given that we do not know every permutation of the algorithms used to rank pages and that there is a domain name and a url to the site there is SEO. The level of SEO is what you are questioning. A site with five pages, all with same title tags, same H1, etc., by having titles and H1's has SEO, but the components are not utilized effectively. At the same time, a site with killer on page SEO that never had a single keyword researched and in which every url, title tag, etc. is based on a keyword query that never is made has SEO at about the same level.
Your question is more about competitive research. How do you know where the traffic came from. A source you could use is Spyfu. I do not like the overbroad way in which some of the PPC results appear, but it would give you some idea as to what they are using PPC for if they are (another caveat is that their organic results are really spotty in my opinion). You can also check any back links to see where they originate from and the likelihood they are driving any traffic. If you know the site and keyword terms, you could use Rank Tracker from SEOmoz, put in the top 10 keywords, then measure them against the sites before and after in rank to at least gain a bit of knowledge, albeit anecdotal to a degree.
Compete.com also has keyword competitive intelligence you can utilize. Try queries on any major engine for competitive site analysis, competitive site traffic, etc. There are a slew of programs. I would suggest using the demo or free versions first as each one I have used has limitations - often these are based on the types of sites my agency is more niche with and it is not necessarily a product of the program being a bad tool.
Best, let us know how it goes.
I wish.