Welcome to the forum.

Your questions will recieve many differing opinions on this subject.

For me, the carrying of any kit, injured or not always comes down to:

Expected distance, expected terrain, expected weather, experience of person(s) involved.

In your particular scneario, it also depends on the type of injury. Even a minor foot/leg/back injury etc may prevent a person from carrying a full load of gear or none at all wheras other lesser injuries may not hinder your gear carrying ability as much.