Does this mean these are the scales you can play in these positions? For example, can you play A, A#/Bb, Cb/B only in the II position?
No, those are just the notes in that position on the G string. There are 3 notes each on the other strings, foe example on the A string the notes in II are B, C/B#, C#/Db. In this and other DB methods, almost all 1-octave scales require at least one shift. For example the C major scale over 1 octave could be played over positions I and II:
C: Position I - 2nd finger 3rd fret
D: Position I - open 2nd string
E: Position I - 1st finger 2nd fret
F: Position I - 2nd finger 3rd fret
G: Position I - open 2nd string
A: Position I - 1st finger 2nd fret
--- shift ---
B: Position II - 2nd finger 4th fret
C: Position II - 4th finger 5th fret
The Db scale, on the other hand, uses the I, ½ and II/III and extensive shifting because there are no open strings available:
Db: I - 4th finger 4th fret
--- shift ---
Eb: ½ - 1st finger 1st fret
--- shift ---
F: I - 2nd finger 3rd fret
Gb: I - 4th finger 4th fret
--- shift ---
Ab: ½ - 1st finger 1st fret
Bb: ½ - 4th finger 3rd fret
--- shift ---
C: II/III - 2nd finger 5th fret
Db: II/III - 4th finger 6th fret
Of course some scales can be played without shifting, e.g. F and Bb major, E, A, B, F# minor
(harm. and nat.) in ½-position. G can be played in position I if you ingore that fact that the requisite open G falls within the ½-position, but since the hand need not move it seems a somewhat technical distinction.
But what is the point of all this rambling on? It strikes me when looking back at the electric bass method books I used in the past that the main focus was on playing 'in position' using a 4-finger method. Shifting was often glossed over - it was frequently viewed as 'advanced' and therefore somehow 'difficult' or 'tricky'. As a consequence, shifting is often the weakest part of an electric bass players technique. With the DB methods, shifting is an integral element introduced, practiced and normalised right from the start. It is rare to see a double-bass player afraid of shifting, but it is commonplace in electric players.