A have a transformer with a screen between the primary and secondary windings and I want to power an audio amplifier with it. My amplifier has no connection to earth, it is powered only by two wires. If I connect the screen only to GND of the power supply (between the filter capacitors) the garbage from the primary will pass to secondary ?
It could be dangerous to use a power transformer that has an unearthed earth screen because if a fault develops, live could become connected to screen and, if the screen is not properly earthed, you have a dangerous situation. What do you know about this transformer other than what you are saying in your question?
Most transformers these days are designed to be "fail-safe" in that they use double insulation techniques to "guarantee" that this sort of fault is virtually impossible. Also, the use of an RCD (UK terminology) or a GFCI (N American) will tend to make the situation less dangerous but why take this risk?
Regarding the noise reduction properties of a screen, this is well-known to be a useful addition and this technique is still used in a lot of designs however, if that transformer is somewhat elderly you cannot rely on it being safe without the screen connected to earth.