Well, when you put the mono plug in the balanced TRS socket, then what would be the ring (3) becomes connected to the ground (1) and it becomes unbalanced. You never ever leave pins 1, 2 or 3 unconnected.
Pin 1 (sleeve/screen) is always ground. Pin 2 (tip) is always the positive deflection. Pin 3 (ring) is the negative deflection, So if you ever reverse pins 2 and 3 you create an out of phase condition.
Now the thing is that pins 2 & 3 in a balanced arrangement, never have a potential with respect to ground, just each other.
So to unbalance a line you connect pins 1 and 3 together.
The next question is where do you do it?
Strict practice requires the line be left balanced at the output (source) and unbalanced at the input. This is called floating a line.
Now I suspect you will have short runs. The only advantage of unbalancing at input rather than source is signal to noise and not sound quality per se.
So I would go ahead and do it the way you intended. If there is no hum or buzz, then you are fine. If there is then you should formally float the line as I described.
That is the way this works.