I suspect this would cause professionalism to develop in the CSA. Baseball will definitely be a professional sport, though with lower wages.
I do suspect baseball wages will be higher overall due to league-jumping, unless the AL, NL, and CL (Confederate League- I do suspect there will be two northern major leagues) collude, which is quite possible, due to league-jumping. I suspect that this would lead to the formation of a Confederate Series.
Another possibility- the Mexican League reaches the Status of a Major League- and there's an AL-NL Series, and a Confederate-Mexican series, then a World Series. (Note, TTL CSA and Mexico are pretty staunch allies against Northern Aggression- and Mexicans have white status.)
I think the Level of baseball would stay about the same- you'd have more teams, diluting talent- but more Mexicans, and maybe more Carribean folks playing baseball, which might raise the talent pool.
The question is what happens after the Northern Leagues integrate? I could see this forcing some social change (cancelling the World Series would be unpopular)- but I can also see it delaying integration.