No. The players have internal skills. When you buy a player, the engine calibrates your team so you cant buy 11 players that scored 40 goals each one last season and expect the same.
The engine will assign internal contributive roles, as key player, assister, a FK man role that will stay attached to aplayer few weeks, another for corners, animations/actions assigned to players...
So you can catch easily a fast trainer, just by listing market players by value and this is related to the visual skills XP, but you can't train a player intentionally and convert him by your own will, in the "best player you ever had". It have to be well programmed by default, and this depend on the internal roles that the engine assign to the players to create a realistic squad.
So yes, if you have enough key players, rarely the engine will give key power players to a new signing. In this case what can happen is theat the new signings will affect the current roles assigned, spreading the contribution so you should notice a change in the key players performance.
This can happen too after a big resources invertment, it can change the order of players of the internal lists of contributive players so all of sudden, you may not recognize your squad, because the massive training could make the FK scorer, stop scoring, the contributive players, if you don't have a clear key player, could be overcomed by other players and stop assisting or scoring all of sudden, cause there can be a change in the internal lists that the game uses to decide how the contribution is spread between the players.
Can seem a complex stuff but, the game have a system, and even if may not be exactly like this, it is really close to this example.