In the US, since the 1970s virtually all technologically-driven productivity gains have been captured by the top 10% (who own 90% of all public equity). (See, e.g., https://www.epi.org/productivity-pay-gap/ .)

So no, little or none of the AI productivity gains will go to workers, barring significant changes in public policy like universal basic income and the massive tax increases necessary to implement it.