The isolation transformer controls where the ground leakage currents and any ground fault currents return to, so its necessary if you can't put in an adequate grounding conductor and ground rod(s) for a TT system. It also doesn't care which way round Line and Neutral are on its primary or even if the primary is fed between two phases of a three phase supply as long as the voltage is correct, and if wired as described will provide a clear Neutral on the secondary side. N.B if wired as described it doesn't provide any 'isolation' for working on equipment, its output should be treated with the same respect as any other mains supply.
Due to its surface resistivity and the 1 Meg resistor in its grounding lead, an antistatic mat is not a shock hazard. However in the absence of a proper ground, you need an equipotential bonding zone, so there is a path for charge equalisation, or even for charge to leak away to true ground via a higher impedance path than would be acceptable for safety grounding if the equipotental bond ties in water pipes, rebar or other structural metalwork.