I too love the old LucasArts games (Maniac Mansion is my fav followed by Sam and Max, the Indy ones are great too). Construct 2 is pretty flexible so building one of these games isn't too hard.
Your challenge is loading large screens for backgrounds. While there will be dynamic content and animated sprites for characters walking around, a large part of the screen is going to be static. So on 800x600 this is a lot of pixels in your layout.
The rest is pretty straight forward. An area to display sprites for commands, a hotspot list of locations on the screen where commands are valid (probably use an Array), sprites for animations and your player character, etc.
The real hurdle with using Construct 2 for this isn't the technology. These games really have a rich story, vibrant characters, and exceptional game workflow attached to them. So technically you can build one, you really need a strong story behind it before you commit to the tool.