If you are only going to use the axe-fx as a noise gate your preset would not contain any amp blocks and so power amp simulation from the axe fx would not be part of the equation at all. You would only use a gate/exp, and fx loop block.
First, press the I/O button on your axefx. Set input source to analog front. Set input 1 & 2 select to Left only.
Set up a patch with shunts from input to output. Place an effects loop block on the shunts, and a noise gate block to the right of the effects loop block.
On the noise gate block, set up your desired settings on pg1, and on pg2 set ‘scsel’ to ‘input 1’.
Connect an instrument cable from Axefx output 2 Left to the front input of your synergy amp.
Connect another instrument cable from the synergy fx loop send to AxeFx input 2 Left.
Connect yet another instrument cable from the AxeFx output 1 Left to the synergy fx loop return.
Plug your guitar into the front of the axe fx.
Set input 1 knob for your guitar, and use the bypass button on the front of the axe fx while adjusting the other three knobs, so that your tone remains intact with the axefx bypassed.
Input2 will effect the level coming back to the axefx from the synergy
Output1 will effect the steady state dry signal going to the synergy’s power amp
Output2 will effect the level of signal going to the front of the synergy.
Play around. You will get the hang of it.
I suggest you find a tutorial on setting up an axefx for 4CM, or find the section of the manual that covers using the Axefx this way. That will hopefully give you a better idea of what you’re trying to achieve.