Technically it's a throttle, the CH throttle quadrant has 6 levers, the one you posted only 3.
The commands you listed are only really usable as button inputs. Even if you turn a throttle axis into a banded slider using CH software (and this is possible from what I've heard), you have to slide the lever down to "press the button" in the lower band, slide it back up to stop pressing that key.
So flaps would continue to try to drop until full, unless you pushed it into the "band that pressed the flap-drop key" and then immediately pulled it back to "neutral" again.
Gear would toggle nonstop if left in the "gear down" band, because there's no gear-up/gear-down difference, they are both triggered with the same key.
So yes technically you can do something like that with the software, but realistically you can't do it for anything other than trim up/down, flaps up/down, or something with separate keypresses that toggle it. And in the examples I just listed, trim already maps to an axis anyways. I can't see many reasons to pursue this path.
There are a couple of other things that are very handy, however. Zoom FOV I have mapped to my throttle on my stick, because I no longer use it for "throttle" -- so I toggle zoom and can precisely specify the level of zoom I want by sliding my thumb up or down.
I experimented with head up/down, left/right, back/forth, but decided to forgoe these in lieu of normal 2- and 4-engine throttle setups with trim. You could try that. In that way you could head up for more lead instantly, or slide head sideways to "look under the nose" in high-deflection shots, etc.
There're other features in-game that may (or may not) benefit from being mapped to an axis.
