This actually does have an affect. Restarting my graphics driver "fixes" the broken G-Sync.
Before restarting, G-Sync is on, like so:
My 3D Settings:
In case these images ever break, under Set up G-SYNC in NVCP, Enable G-SYNC Compatible (Enable for full screen mode) and Enable settings for the display model are checked. Under Manage 3D Settings, the Global Setting (which my games are set to follow) for Monitor Technology is set to G-SYNC Compatible.
These settings are supposed to activate G-Sync like they say, but they can "break" and not apply any variable refresh rate despite being activated in the settings. You can tell by turning on the G-SYNC Indicator setting and the OSD Frame Rate setting (both will show if G-Sync is actively working). It seems that with this monitor and multiple other Alienware monitors, G-Sync being on actually reduces input latency, but if you want the fixed, highest refresh rate, that's not good. So you need to "break" G-Sync by changing the setting multiple times until it stops working but will still "apply" the lowest input latency.
But yes, using restart64.exe restores the G-Sync function so that it works like it says it should. Now I have to break it again.
For those who may find this post in the future, yes, G-Sync being on gives you lower input lag on this monitor (AW2723DF), but you need to find a way to have it on in the settings, but not actually working. On top of that, the monitor will change your Nvidia Control Panel setting to "Fixed Refresh" automatically so you'll need to make sure that doesn't happen while you change the G-Sync settings or restart. I suspect that's why the input lag felt so random. Hopefully that's everything but I'll update if I find out more for posterity.