So, yes, you could make a complete website experience in Construct (I believe having read on this forum that some users already did btw) - it even supports responsive elements that automatically adjust to the screen size. In that sense it actually outsmarts Flash. The only real issue would be SEO, because a Construct built web page would be quite opaque to search engines: there is no regular html structure.
Again a comparable situation compared to Flash (which has dreadful SEO)!
It would also be harder to update its content. Much harder - although the Ajax behaviour could be a great help here, and mitigate this issue somewhat. And for a static highly interactive web experience, where SEO is not that important, Construct is a good alternative to pure html and css or Flash.