Yes, that is more or less correct.
Mind that, when you say "turns on" or off, this process happens gradually, over time. Not digitally, and not instantaneously (nor simply delayed, either).
If it simply were on and off, it is plain to see that it can never be stable, it must oscillate. As it happens, there is a happy medium between the two extremes (uh, taking something like purely proportional control -- like replacing the voltage regulator with a (very wasteful) resistor divider -- as the opposite extreme), where for the right degree of gradual change, it settles into a stable, quiet state.
There is, of course, a body of mathematics dedicated to the study and calculation of these processes -- dynamics. While we can wave our hands and make a simplified, colloquial statement, we must be careful not to take something too literally, but we should strive to understand the underlying process.
Regarding the resistors -- I mean, it's still a resistor divider. If we assume the REF pin has some voltage, and the +in pin draws no current, then its voltage must be the divider ratio times that input voltage, simple as that.
A practical circuit should of course have current limiting, and maybe foldback limiting at that, some transient protection, and maybe thermal protection, or an enable, or other add-ons as suits the end use. The main reason those aren't shown is because they complicate a simple
idea. Appnotes have a careful line to follow, between showing an idea simple enough that any joe schmoe engineer can remember and understand it, and showing something that's complete enough to be usable as a drop-in circuit. (And I suppose manufacturer FAEs are one bridge between those extremes... nice, if you can get a visit from them.)
So, I would caution against using the circuit verbatim, if you happen to need its function; but it's a fine core, and can be built upon without too much trouble. Compare with other circuits like classic LM723 supplies and whatnot (which usually include current limiting, and often use emitter follower outputs just like this does).
Tim