My understanding of overfitting is that it's primarily a problem of the model being too flexible (i.e., having too many parameters to tune). I say "primarily" because there are "early stopping" and regularization methods that can help ameliorate overfitting in some cases.
By overfitting I mean: parameters take wrong values.
For example: reset all parameters to zero. and tune just one parameter (pawn value). The result will be overestimated, 187 to say a number. Next tune the knight value, it has to be over the pawn value, the same of a bishop and below a rook or queen. All of them set to zero by now. So the knight get a value of say 217.Each step incorporate a new feature in the eval, being better it is far from optimal. Each time we try to explain a wrong evaluation with the wrong feature we get a bad value.(pawn value against the whole evaluation).Quick convergence, very few parameters, overfitting ? may be this is not the correct word.
Is it able to leave a local optimum again or will it optimize towards it and then stop
I forgot to say that we need a minimun number of votes to award an increment. This number controls the inertia of the system. If the number is small, as the data is entered the parameters bounce to adapt (Quick convergence and keep the system in the local optima.). If the number is large, a parameter only move if there is strong evidence it must do this (low speed convergence, no local bouncings.).
For sure, it is not the ultimate tuning method, but it show that other "ad hoc" systems can work fine.
Another example is that you can tune without minimizing the error function: You can tune maximizing the correlation, you do not look then for a close matching of values but for a similar shape of the evaluation function.