Sure the poor will grow more poor, and also have a lot more free time due to not having employment. That's not necessarily a good thing, but it does agitate for both the optimistic and pessimistic views being likely at once in the future.
I assume you're advocating their support through some social safety net that provides them with basic necessities.
Because currently, not having employment is a major loss in free time: you spend all your time trying to meet core needs like food, shelter, and clothing. Where an employed person can simply order take-out, hire a contractor to fix their house, and buy new clothes as required, an impoverished person will be scraping together safe food and trying to cook it to be palatable, sheltering in uncomfortable or unsafe places, and repairing clothes that are long since worn out. And if they do go to work, they earn a pittance that's insufficient to pay rent, much less afford luxuries like prepared food, home ownership, or durable clothing.
Unless you're extremely optimistic about social services improving, the poor being poorer puts heavier burdens on their time, not lighter.
Automation if anything makes this worse since people will often decrease to fill the need instead of hire more.
Work to live or live to work.