I'd imagine it's possible to fake yeah, maybe anything that has the effect applied has a parameter to set "how far" they're spread apart then either do anaglyph (red-blue for each eye old 3D style), or separate eyes in a VR headset if Construct ever supports that.
The browser standards are to blame, not really C2s fault if you'd ask me. So far Ashley did try his best with supporting
the newest browser based features and I doubt that he would just ignore a new feature like this.
I guess since Facebook is doing stuff with VR we can expect to get official VR support inside browsers "soon",
it is only a matter of time and money from both sides.
I also believe that the N3DS had "3D popout" support for 2D games
but I'd have to find my N3DS and look for the games if you really care about examples anyway.