No, the GUI does not have to be running for Swar’s to create plots. It fires the chia.exe in the background to produce plots.
Swar’s is a plotter. It does not farm. If you want the same system to run plots with Swar’s and farm, the GUI will need to be running or you know how to run farming in the CLI.
I don’t think the active plots running in Swar’s show in the GUI. But I have never tested this.