Broken stem

yeeess, it definetly will survive that. Its a thing many people like me do on purpose. Not optimal since u also trimmed away stuff and the plant will be stunt for a bit, but after those branches will come up even stronger and take all the potential of the stem u took off. If you are lucky, your plant has strong genetic and recovery and you will be left with the same amount of harvest or a bit more and way better plant structure. But normally its a bit less harvest, since autos dont have time to recover that much in there limited growth phase. But it will definetly survive, no doubt.