In any given system the total momentum will remain constant.
For the case of Sammy Sosa, a corked bat is lighter and might therefore be swung faster, but momentum is mass multiplied by velocity, so the higher velocity will be cancelled out by a lesser mass.
Also the bat is only in contact with the ball for about 1/1000 second, so the “trampoline” effect of the cork will not be great at all– the time of contact is so short.
The cork center can have a negative effect too, since energy that makes the more springy bat change shape will not be available to propel the ball forward.
The benefits probably are mostly psychological, since many ball players are superstitious.