No. Divisions 1-25 were regular Army, 26-50 were National Guard, and 51-108 were draftees. They were not designated according to MOS. Some of the divisions were never actually populated, so there are gaps even within this.

Later on, existing divisions were designated according to type. Infantry is the 'default' designation. Cavalry units were designated, then Armor, then Airborne, and finally Mountain. I have no idea when Artillery got its own designation. Some units subsequently were designated Air Assault, and this includes the 101st, but it kept the Airborne title to honor the unit history.

Other branches have other policies, but this is how the Army structure evolved.

The military explicitly does not number their units in numeric order as a counter intelligence measure.

In the book 'Surprise, Kill, Vanish: The Secret History of CIA Paramilitary Armies, Operators, and Assassins' by Annie Jacobsen, she mentions this effect when the US Army stood up the secretive 10th Special Forces after WWII. Even though it was the first of its kind the idea was that if the U.S.S.R found out about it they would worry there were 9 other such groups.

This differs by branch of service in the United States.

The UK actually has its regiments ordered by seniority