This is an issue that comes up all the time.  The simple answer is, absolutely!

Most injuries will only effect 1 area of the body, so by actually training the opposite areas it will be even more beneficial.  Often times the cause of these injuries is an imbalance between the front and back muscles anyways.

The posture assessment we do before each client signs up is very important in addressing these issues.  We almost always see issues in the shoulders caused by bad posture and the natural aging process.  So this shows we need to focus even more of rowing and pulling motions, and less on pressing.  A client battling a shoulder injury can almost always still perform some of these movements.  Then over time by doing more pulling and less pressing, it should help with any shoulder pain.

Knees are another very common issue.  We always also look at the hip angle of each client to identify if either they are naturally putting too much pressure on their knees, or to identify if there is an imbalance in strength between the front of the legs and the back.  Again almost every time we see clients with stronger quads than hamstrings, which can lead to knee issues.  So just like the upper body, if we put a larger focus on hamstring and glute movements, it will strengthen the back of the legs and hopefully help with knee pain as well.  These motions almost never hurt the knees anyways, so it allows us to really focus on working the lower body even with an injury.

So a long story short, the upper back, glutes, and hamstrings are the muscles that should be worked the most anyways to help balance out posture issues and potential injuries.  We all walk forward and push things forward, lean forward, even exercise these front of the body muscles more because we see them.

Even if you are 100% not willing to train your upper or lower body during a session, we have lots of other options you can try.

Cardio/abs specific workouts are very popular for clients battling injuries that strength moves can make worse.

Boxing can also be a very fun and intense upper body and cardio workout.

Rehab workouts to slow down and really focus on specific areas that need to be stretched and targeted.  Balance and posture moves are also very helpful here.

You could even just work with your trainer on nutrition advice and plans.

I understand that maybe some of you feel like if you can't give things 100% it is not worth it, but compared to sitting on the couch doing nothing, this is much more beneficial.

Also what ends up happening is you take a month off from exercising because of an injury, and then come back and request exercises that won't hurt the effected areas.  This is all things we would have done anyways.