Curious, is the reason that a C2 website would have similar disadvantages as a flash website because of the canvas framework?
It's simply because it's not an ordinary HTML page. That means to Google, it looks like an empty page. It can't easily access any of the content.
You can probably use HTML5 for decorative banners or adverts and such, but I still wouldn't even recommend using it for your site's navigation menu. Since Google can't see the links inside it, it might not even crawl your entire website! And again your pagerank could suffer significantly.
We can't control what people use Construct 2 for, but I do believe it's the wrong tool for the job if you want to design websites. It will only cause your website to be less successful, unless you use it for decorative or non-essential things (or games, of course!)