I agree with 99, all tubs should have access behind them anyway.
I would cut a big access behind the tub and make a nice cover panel so you could hardly even know it's there. Go from the floor up several feet so you can work in there and also get a good view of the entire hidden area.
After observation then I would make a decision from there.
I do agree with Eplumb that his main focus is on the leak but it's always a different story if the leak is in my house and I have to repair it after the leak is fixed. Take your time and think it out before chopping big holes in your house.
No Warranty Means- If it breaks in half you get to keep both halves.