Hi Ray,
Congrats on the purchase - I am fairly new to drones as well, but I have a long background in photography, so thankfully pretty much all the same principles transfer over.
At 180 degrees (sun behind you) polarization will be nonexistent. Between 90 degrees to the sun (where it is strongest) and 180 degrees to the sun (where it is weakest), you have varying levels of polarization. Further to this you can rotate the filter itself to control the amount of polarization, because sometimes the polarization effect can be too strong (it can make oddly or unevenly dark skies, crush blacks, etc.) A quick check is to make a "gun" shape with your thumb and index finger- point your index finger at the sun, and anywhere you can rotate your thumb to in an arc will have maximum polarization (the entire circle around the sun will be equally polarized).
The Mavic Air has a 24mm lens equivalent, so it's not quite wide enough to start running into problems with heavy vignetting or uneven skies with a polarizer, so there are a couple less things to worry about there that are concerns in the traditional photography world when using wide angle lenses.
I just use ND's most of the time, but polarizers can really make your footage pop if used properly. For example in tropical climates where you can often see the coral reef through crystal clear water, I would probably be utilizing a polarizer. Sometimes foliage can have distracting reflections especially on large leaves, and a polarizer will help remove that too, but it really does depend on each individual scenario. That isn't the only use for them of course, just one example. If you just want to set it and forget it and not worry about direction, ND's are easier to work with because all you have to worry about is exposure. You probably aren't going to ruin your footage by flying in all directions with a NDPL, but you may not like the inconsistent look as polarization changes throughout. Chances are anytime you want to use a polarizer it will be brighter out - I think an ideal kit (assuming you don't want to just buy every filter) would be ND4, ND8, ND16, ND32, ND16PL, ND32PL. If there are certain conditions you never shoot under, you could omit one or more of those as well (i.e. if you never shot at sunrise/sunset, you could probably omit the ND4).
A LUT cannot replace a polarizer - that is one thing no software can do even today. You can duplicate the slight contrast/color bump you sometimes get with a polarizer, but it is impossible to remove reflections in post processing and mimic that effect of polarization, so if you want to do that, you have to use a polarizer. Personally I get away with normal ND's most of the time, but if you have a well planned flight path and favorable conditions for a polarizer, it can make a significant difference to the footage.
Hope that helps.