To get the benefits of a balanced connection, both pieces of equipment being connected must have balanced connectors (TRS, XLR, etc) and both pieces of equipment must support balanced connections.
In Balanced connections transmitting components send the signal (+) on the tip and a polarity inverse (-) copy of the signal on sleeve. By summing the + and - within the recieving component, the noise can be eliminated leaving the original signal minus any inducted noise that was picked up by the cable acting as a EMF antennae (10 + -10 == 0). The point: if both components are not balanced and connected with balanced cabling, you do not get this noise cancellation.
Additionally, I believe that TRS cables due to their twisted pair wires coupled with a polarity inverted signal makes the cable more resistant to inducting EMF noise. In other words, it is my understanding that the twisted pairs minus the polarity inverted signal would offer no resistance to inducted EMF noise. I am not 100% sure on this particular paragraph. There is contradictory information on the web, but if it is correct this would indicate that if the sending component is not balanced (sending a polarity inverse copy of the signal on sleeve) you would not get EMF induction resistance.
The short of it is this: a balanced out on the G75 to input 1 you may provide some EMF induction resistance but the connection will offer no noise cancellation because Input 1 is unbalanced and therefore the connection is unbalanced
You could use G75 to Input 2 on the Axe III (XLR -> XLR) to get a balanced connection.