Can I use El Capitan on a MacBook that is shipped with Sierra? I just purchased late-2016 15' MacBook Pro, which is shipped with macOS Sierra as of now.

However, Karabiner, a software that I deeply use every day has a serious compatibility problem with macOS Sierra, and thus I couldn't work on the mac productively enough. 

So I would like to use El Capitan on the new MacBook Pro if at all possible. At least I was able to restore my TimeMachine backup from El Capitan on the new mac. Is it possible to run El Capitan on a Mac that is shipped with a newer version in default?
Nope, the 2016 15-inch MacBook Pro can not run El Capitan. The oldest it can run is 10.12.1 (16B2659). 

If you attempt to boot El Capitan, it will present you with the prohibitory symbol.