normalization/denormalization for linear regression problem
I think it is ok, as long as your training and test data have the same maximum values for every feature, approximately. The idea is that the scaling has to be done with the training set (remember that using the test set for anything that is not testing is illegal, not even for scaling).

So, you actually fit $y'$ as a function of $X'$, and you have a model that maps properly $y' = f(X')$. When you get your test data, you just obtain the predictions by doing $f(X_{test}')$. As the paragraph before states, if you have that $scale \approx scale_{test}$, then you can just recover $y_{test}$ by doing $y_{test} = scale \cdot f(X_{test}')$.

Edit: Don't worry about nonlinearities

Even if the function $f$ is highly nonlinear, it is a function capable of mapping $X'$ to $y'$. If you trust this function and trust the fact that $y = y' \cdot scale$, then there is no need to worry about the way $f$ acts, as function composition makes sense for all kind of functions, both linear and nonlinear.