I'm not so sure that is a factor....
Since Besiktas we have played on the following dates: December: 14th, 17th, 20th, 26th, 28th. January 1st, 5th. 7 games in 23 days, biggest "rest" gap between the 20th and 26th. No different to having european matches thrown in between league games. (we played 6 games in 19 days leading up the 11th Dec, Besiktas).
I'd like to give the players and the manager a bit more credit than just to suggest we're playing well because we aren't playing an European games.
The difference is that the teams we were playing during December were also playing roughly the same busy schedule. The playing field was even as everyone had less rest and less time to prepare.