You can. Both 'damaged' and 'injured' are fine. There are a few points to consider:
1) The past perfect forms could be used because those events referred to by the perfect occurred prior to their conjugates, thus serving the form's function:
a) He damaged his knee before he began his two-year hiatus.
b) He injured his knee before he fell down.
2) Though we may use the past perfect form to indicate clearly which order a set of events occurred in, we need not do so. The audience will generally be able to interpret such ordering by factors beyond the sentence.
3) Sometimes we have good reason for not using the past perfect form to indicate ordering. For example, the past simple may suggest a stronger temporal connection between events.
Looking back at your sentences in question we could well opt for the simple. Doing so would show us the strong connection between:
a) The damaging of the knee and the consequent hiatus.
b) The injuring of the knee and the consequent fall.