Does GNOME or KDE desktop enviroment matter, at running a BitcoinCore node?
The particular desktop environment does not have a direct impact as long as you have the necessary libraries for running Qt applications.

On Debian (or Debian-Based distributions, such as Ubuntu) the following command should install the dependencies necessary for the UI:

sudo apt-get install libqt5gui5 libqt5core5a libqt5dbus5 qttools5-dev qttools5-dev-tools libprotobuf-dev protobuf-compiler


Those are the packages used by the bitcoin-qt package. Source