I don't want to stir up too much trouble
, but a lot of those firmly opposed to training off rock have also posted about a wide array of chronic injuries plaguing them...this is not normal and stems from over straining tissues before they've had a chance to over-compensate from the previous injury. Do this enough times and your body can no longer heal properly.
When rock climbing, especially on lead, you don't have the opportunity to go "I'm over-working my joints, I need to back-off". Instead, you're forced to continue past the point of injury or risk even greater injury in a fall. In a gym, you can stop the moment things twinge or feel off, and let those joints/tendons heal properly before continuing.
Conversely, excellent rock climbing technique will let a relative weakling tackle 5.10s (past that strength is pretty much essential). So practicing regularly on rock is critical to mastering how to get the most out of what strength you have.
For me, when I trained on rock exclusively, I kept getting mild pulley injuries in my fingers. However, through strength training that emphasized compound motions and grip strength, I was able to go out this season and hammer hard on crimpers with no pain at all.
So, for me at least, strength training has been very helpful. And there are plenty of exercises relevant to climbing: pull-ups, dips, rows, supermans, and crunches all help with core strengthening and strengthening the upper body. Wrist rollers can be done to strengthen the forearms and the tendons in the fingers. I've also found nothing matches running up mountains for leg strengthening and improving over-all stamina.