The text...
Joe's been chasing some women ever since he was young
...could have at least two different meanings. Which applies would be largely contextually determined, but #1 below (the one Quirk et al are apparently referring to) would be strongly implied by very heavy stress on some...
1: There's a specific set of women that Joe has always chased after
2: Joe's always been chasing after some woman [or other], but the particular woman he's pursuing changes from time to time
Note that #2 above is the same as...
I met some guy in the pub last night who told me [interesting fact]
He's always got some excuse for why he can't help me
...where some is a casual (often, "dismissively insulting") reference to any randomly selected woman / excuse / whatever. We tend to use singular for the second meaning, but that's not an unbreakable rule.
Effectively, if sense #2 above is intended, the only significance of including some at all is to imply contempt for the kind of women who would allow Joe to flirt with them and/or Joe's lack of discrimination when it comes to choosing potential romantic partners.
Without some, the assertion could be approving, disapproving, or neutral towards Joe's long-term philandering. Using singular some woman (often followed by ...or other) maximizes the contemptuous implication.
There's also a (very unlikely) possible implication to including (not particularly stressed) some that could be intended to mean Joe chases multiple women at the same time (together as a group, or by going out with them on perhaps different days of the week, without them knowing about each other).