Does dry-brushing really do anything...

IMO, it's more of a ritual than a necessity.  I agree that the type of dust it removes does not affect the playability, although I'm sure Doug Deacon would disagree.  Of course it is possible that a piece of crap somehow got onto the record that the brush would catch, so I guess it pays to take the five seconds and just do it. 

Depends on the weather/humidity level.

The Audioquest brush works well during the Summer when the humidity is higher, but during the Winter in the Northeast it creates static on the LP, which then adds the Zerostat to the ritual.

I stopped using a dry brush a few years ago, and instead have been using Last All Purpose Cleaner after each play.  This works well to pick up any dust before putting the LP away into its anti static sleeve.  I dispense the Last cleaner from a small spritzer bottle rather than the dropper bottle it comes in, for better control of the amount of cleaner that goes on the brush.

The old discwasher with a few drops of solution on the edge kept my records clean enough for decades that most still look and sound great.
For me, no dry cleaning process I have ever tried (Audioquest, Hunt) works as well. Ultrasonic wet is the ultimate.

I use a Hunt brush with a spritz of distilled water from a re-purposed eyeglass cleaner spray bottle.  This is the kind of bottle you get at the optometrist and puts out a very fine mist.  Once empty of the eye glass cleaning solution, rinse thoroughly and fill with good quality distilled water.  Hold the bottle 1-2 feet away from the brush and spray in its general direction to very lightly moisten the brush surface.  Helps pick up dust rather than just push it around.  

By the way, ticks and pops are often - though not always - the result of wear from repeated playings eventually exposing voids (tiny unfilled pockets) in the vinyl that were formed at the time of manufacture.