In reply to KS.

I don't think your question is well defined. For example, if you have a linear regression model for Y = b0 + b1*X, you can't calculate the sum of "all predicted values" because X is infinite. If you restrict your attention to finitely many X, then the answer is yes. If you restrict X to a compact domain, you can ask for the "expected value of Y" conditional on X being in the given region. I suspect your question will make more sense if you recast it in terms of expected values.