I am an expert. Or at least an upholsterer. When you say the leg broke, what broke? Did it snap? Did it push into the sofa? Some legs have a bolt sticking out and screw into a T nut that is on the inside of the sofa.
Sometimes that punches in and just spins when you turn it. You have to pull the bolt out as hard as you can and try to get those prongs to grab wood. Most legs are one of 2 sizes. You could find another leg and bolt it back on.
It may also be a block of wood that screws to the bottom of the sofa. The holes are probably hidden by the felt scuff pad thing.
There is absolutely nothing wrong with propping it up on a brick or book or whatever. If you want to be less ghetto, take a leg from the back and move it to the front so your guests can’t tell your couch is propped up on blocks
Yes, it’s repairable, but it’s fairly involved. A fair amount of the sofa needs to be “undone” to get the arm off. How much work that is depends on how the couch is constructed. Then it becomes a matter of matching the leather, which probably won’t be possible to make it invisible.