No, Not Quite. The Transformer should have a Faraday Shield internal to it's construction it is a foil Shield, carefully insulated and wrapping the core between Primary and Secondary windings the ends are not connected so it will not be a 'shorted turn' rather an electrostatic barrier between Primary and secondary. It is also mandatory to use a Good Quality dual winding common mode choke in the Primary winding with filter capacitors and sometimes in the secondary as well (Yes I have seen both utilized???) the Ground Lead is a part of the frame of the transformer and sometimes an electrostatic drain... a 1 M ohm resistor and 100 to 1000 pF in parallel from Ground to the metal case. All other grounds MUST Connect in a Star layout directly at the PSU Negative terminal (Or Common if you are using a Split Supply). The Star topology as you know forces all returns to one point rather than the more common "Daisy Chaining" this Grounds noise rather than 'sharing' it with everything else. This is also necessary because of thermo-electric (Seebeck Effect) precautions. I refer you to this Wiki article which should help especially if you ever need to design "Very Low Drift DC Amplifiers" it is one of several "Gotcha's" inherent.
http://en.wikipedia.org/wiki/Seeback_effect#Seebeck_effect and I remind you of what my Engineering Prof used to say... Good Design is a series of Successive Approximations to the Solution.
IMO
Doc