Hi George,
The monk Analāyo also addresses your question in footnote 69, Chapter VI, "The Body" of his book on the Satipatthana, his PhD thesis.
George:
The below sentence from MCTB confused things a bit:
"In short, you must master the first jhana as a minimum basis for beginning the progress of insight, but this is all that is
required for enlightenment."
Analāyo references Kheminda (1992), who references "Soma (1995), p. 360:
the placing of the first tetrad of the Anāpansati Sutta at the very beginning of the two main Satipatthāna Suttas is a clear indication of the necessity of at least the first jhāna...the development of insight is impossible to one who has not brought into being at least the first jhāna."
But if you are noting well (which becomes very rapid), then this noting becomes vitakka (mind landing on the object again and again and again and again), which when enough of these landings are strung together with fewer departures...voila, you have vicāra, sustained attention to the object (the breath). If you approach noting with piti (joy/zest) and sukha (comfort/calm happiness), then the mind will grow to like these short exercises and extend them into longer efforts (10 minutes, 20 minutes, etc).
Does the noting develop samatha jhana?
It can, but anapansati has a specific progression that starts with piti and sukha, especially.
Yet noting can be useful to people who are not doing jhana training. Lacking support of piti and sukha, noting can fall prey to dullness and/or conceptual perseverations, as with counting the breath. Analayo describes possible (not inherent) hazards of counting as potentially being able to "
...dull the mind stimulate the conceptual activity of the mind instead of quietening it." The quoted words here come from Analāyo's footnote just above the last, footnote 68, Chapter VI, the Body.
So just be alert to that. I think if you add piti and sukkha to your approach, meaning when you start you start your exercises with some eagerness/zest/calm happiness (I started jhana work after my physical workouts in order to get the natural benefits of exercise pleasure) then I think you easily can avoid dullness and conceptual perseverations, and move into actual jhanas naturally, little by little, like all trainings

.
Jhanas are therapies designed to temporarily abate mental hindrances, welcome the mind to its own self-study and the insights of studying one's own mind, and to train one's own mind in a friendly, systematic way (with piti and sukha in the beginning).
Like any skill, jhana takes regular, reasonable training. So just like if I start to practice guitar today, the results will sound bad for a few weeks --- and I should not lose my respect and friendliness for my effort even though it sounds awful in the initial investment period --- there will be noticeable improvements if I keep at it.
What do you think?