The Awesomium exporter never changes the actual display resolution. It will just set the window size to the size of the monitor, and if you use letterbox fullscreen that means the game will fill the whole monitor too.
In practice this is no different to how it would appear even if it forced the resolution; CRT monitors are very rare nowadays, and most modern monitors only have a single native resolution, and will bilinear filter different resolutions and basically stretch them to fill the window - exactly what Construct 2 would also be doing.