Keeping baseline as predictor with change score as outcome in this peculiar scenario

It is generally recommended that baseline should not be kept as predictor if change score (final - baseline) is the outcome variable. However, there are many instances in biomedical research when one feels that baseline may be affecting change and it may be biologically important factor.

Consider following scenario also:

If a child has height h1 at baseline and we give a height increasing drug. The change in height has to be positive (since height cannot decrease). Moreover, it will be close to initial height (hence not independent). So final height cannot be random. While we may assume the change (increase) to be random in a distribution.

1. Can we test "change ~ h1 + trt + age + gender" in this scenario? If not, why not?

2. Similar example can be given of weight; only there change can be positive or negative. Does that make a difference to approach?

Thanks for your answers.