Q.

Is it possible to have balanced Aux sends on the GL2200?

A.
You can achieve balanced aux sends by using the monitor mode, reassigning the auxes via the group faders and the group outs. The groups then get controlled via the aux masters and output via the aux TRS jacks. 

If you want to balance your aux sends permanently, then you will need one SSM2142 IC (A&H part number AE0302) for each Aux output.
The chip would need to be fitted in the appropriate position, and then two links cut to activate each balancing chip. 
Without the chip fitted, you will get much better noise resistance than an unbalanced line if you use balanced cabling, but you will not get the higher output level of a fully balanced output.

(The SSM2142 is an integrated differential-output buffer amplifier that converts a single-ended input signal to a balanced output signal pair with high output drive)