Long story short, yes, in the long-run output per worker will grow at the rate of technological progress.
This happens because marginal output from capital and labour decreases over time (marginal diminishing returns to L & K), eventually reaching a steady state where output per worker stops growing.
Thus, at that steady state point, technological progress allows output per worker to keep growing even when capital per worker remains constant.
In the short-run, this doesn’t necessarily apply, as changes in capital can immediately affect output per worker.
This is all explained in much more detail in my article on the Solow growth model—check that out here.
Otherwise, hope this helped, and leave any questions in the comments! Check out my other articles on economics here (useful for studying, or just learning).
