From my experience, productivity will indeed increase but whether in future it would skyrocket is still unknown. Certain repetitive administrative tasks would be taken care of in the background. It also appears that AI has some level of creativity, which would be useful to improve certain non-routine discretionary tasks (but with human oversight). Beyond that, AI is still limited to human inputs. I won’t trust AI (yet) to perform tasks that are subjective. In conclusion, yes, AI will improve productivity, however it still depends on how much a company needs to pay and if that cost will really be translated to savings.
What I expect to see?
A lot of companies cutting jobs related administrative and HR, slowly moving into IT. This is already happening. With future robotics and further automation, production workers performing simple, laborious and repetitive tasks. Then, cuts will slow down for companies to check costs of AI tokens vs benefits. We might see rehires if cost increases.