Actually, according to PC Gamer, you can. I believe they also offer a service where they'll split the profits between you and them, them getting 20%, and they'll handle the publishing side of game development.
I've been debating using it, as it has great porting options. My main concern is programming. I've presently got everything else at my indie studio for making a tech demo in pretty much any engine (we're so far using UDK) except a programmer.
I know programming methodology but I have no languages memorized as of yet. I've actually made several proof of concept demos, and am now working on an adventure game as my senior project that I'm hoping to see released by June. If you have the right people and the right engine, you can work around it, it just isn't easy. A lot of indie devs are hoping Unreal Engine 4 will change that.
With most engines. Construct doesn't require one, but its one of the few engines that doesn't. We're in the process of getting an adventure game done, then we're going to focus on trying to get a programmer so we can get our initial game ideas rolling. Right now, we honestly do need a programmer if we're going to make anything in 3D.