Happens all the time
"I know that one should expect swings of 100 units, but has anyone actually experienced being down more than 100 based not on poor play but on simple variance (natural swings in any game of chance)."
Probably everyone on the board! :-)
"In other words: if someone was to flat bet and count only so that the player/house edge is 0% and played 4 hours per day"
So, let's say 400 hands daily.
"for months flat betting $1 each time,"
Let's say a year: 365 x 400 = 14,600 hands.
"what would be the most units down at any particular point before things would cycle back down close to zero?"
See my other post. You do NOT expect things to "cycle back down to zero." Instead, the more you play, the farther from zero you would expect to be. If I play ten hands, just how far from zero could I possibly be? Ten. If I play 10,000 hands, would you expect to be within 10 of zero, or farther away?
"What is the highest number to expect theoretically? (Maximum Bankroll needed to allow for natural swings)."
After 14,600 hands, the mean result is zero. One s.d. is sqrt(14,600) = 121 units. So, you have almost a 16% chance of being down 121 units at the end of the year. However, you have double that probability, or a full 32% chance, of having been down 121 units at some point during the course of the year! (See BJA3, and the discussion of the "premature bumping into the barrier syndrome.")
There is also a 4.3% chance of being down 2 s.d.s at year's end, which is 242 units. So, there's better than one chance in 12 that, sometime during the year, you will have been down 242 units.
Get the idea? Choose bankroll accordingly. Season to taste. :-)