For website use, I think that there would be too many issues using Construct 2. But it probably depends on what you want.
Nowadays, reponsive websites are the new black - and this is either impossible or extremely hard to attain, using Construct 2 as your only developing tool.
If you want to combine Construct and HTML5, CSS3 etc. - then yeah, it can be done. But then I'd much rather go with jQuery for fancy effects, and frankly I'd avoid canvas and WebGL. But it depends very much on what you want; fx. if you want your users to navigate with a plane to open up certain parts of your website, Construct can easily do the job. But you want a more traditional approach, I'd advice you to do it more... traditionally.
Also, as I make everything dynamic and my backend is PHP/MySQL, I'd personally be at a loss of how to to that with Construct. Maybe I'll learn some nifty tricks after a while; I'm a newcomer to Construct, but a seasoned web developer. ^_^