Hi,
In a toroid design any material that can conduct current and goes through the center constitutes a single turn. This means that if there are wires connected to the socket any they go through the core those wires will be affected, and any metal that makes up the contacts will be affected.
How they are affected depends on how they are situated inside there. If one wire goes through the center series aiding it will add to the voltage, if one goes through series opposing it will decrease the voltage. If one goes one way and another goes another way they may cancel each other out.
So as you can see, it's a little hard to predict without having a drawing of the exact construction and without knowing what the turns per volt ratio is. This means a simple test is on order. Simply allow the conencting wires a little more slack when the thing is first built. Try the device with the socket NOT in the center of the core, measuring the voltage and input current. Then push the connector into the center where you need it, then measure again. See if there is significant change. After it is pushed in, you also have to test for heating. The eddy currents in some metals will be much greater than in the toroid metal, so after running for several hours see if the socket feels hot or even starts to melt.
My gut on this is that it wont matter, but tests can be done to be absolutely sure of this or prove otherwise.