Yes, those training level increase will be gained by those 40% reserve players even before we have completed buying the full squad in the new season.

What I did is upgrade the first skills in attack, defence and physical&mental to pro level first. The increase will not be as good as a higher level account, but only some 10%-15% less in level 2 onwards.

And 1 side-note on selling players. When selling players to system, the default value is 99% of face value of the player. There is a random chance of getting an extra value in 10%, 20%, 30%, 40%, 50% and 100%. The younger the player, the higher chance of triggering the higher % in extras. Bought an 18yo for 2.5m in season 2 with 1T (That was an impulse buy as it was just 1T but not fit for the team) and decided to sell after 1 day, and sold at 5m. That extra helped a lot then, so maybe new managers would take age into consideration when they are buying players to play in the season and also want them sold by end of season.