Yes, it essentially is connected to "ground". Yes, it is there to provide an offset adjustment.
Your "ground" is really the +2.5V "pedestal voltage" (by the way, where IS that being generated in your circuit? I don't see its source point anywhere). Opamps and instrumentation amps in particular want a bipolar supply. By giving it that +2.5V reference as ground (0V), the voltages on pins 7 and 4 look like a + and - 2.5V supply.
It can also be used as an offset adjust, it is part of an internal divider circuit and by raising it very slightly above or below the +2.5V reference, it can be used to cancel out offset in the final stage of the instrumentation amp.
In your circuit, it is used in conjunction with a high-pass filter. This is to reduce DC offset problems typically caused by electrode galvanic voltages.