One of my Eighteen year olds gains 3 skill points for each hard training session, 2 of them only gain 2 skill points each training session.

One of my Eighteen year olds is on skill rating 32, two of them are on skill rating 40, I have saved skill points for all 3 of them (the 32 rating player has enough saved SP to get him to 41 rating).

Not conclusive, but it looks as though skill rating does have an effect on how many skill points a player gains, and unassigned skill points seems to not have any effect.