sorry for this plane question, but is it actually possible to conect a Electret Mic without any capacitors etc. to the input of the arduino just to read out if there is any signal or if there is none?
Or does it work with the Breakout Board for Electret Microphone like that:
no
electret microphones need some polarization that why you need a capacitor
electret microphones outputs a very very low signal (around a mV) so you need some amplification
The microphone on the picture looks like the BOB08669 SparkFun Electret Microphone Breakout - BOB-12758 - SparkFun Electronics from Sparkfun. I personnaly own one which works perfectly.