No, it won't. The sooner we shift from labor to education as our source of social dignity the better. Let's pay people to go to school rather than to flip burgers.
The key reasons to automate, is it allows us to make this type of food available to masses for fractions of the cost of what it would take for a human to grow it.
There's nothing wrong with people doing low paid work. Those of us who can't stand it impose our values on others. I worked a lot of manual labor while studying. I worked on mowing crews who spend their lives mowing the same pieces of grass over and over. You'd think they hate it but they were happy to work a low stress, secure job and just do their hobbies in their off time, whether coaching kids or building model railways. Of course that's not everyone but it's wrong to pretend we can walk in everyone's shoes.
You will have difficultly securing quality education for your children, either because you can't afford private schools, or because you can't afford to live in a location where the public schools are of high quality.
You also are likely to be living pay-check to pay-check (sometimes even less, with pay-check lenders taking their vig), and only a small health-emergency away from becoming bankrupt, and quite possibly homeless.
So, no - I think there's a lot wrong with people doing low paid work. It might be okay for the young, or students, or the retired, but for most adults, low-paid menial work on a prolonged basis in the United States is a financial and personal disaster.
As long as that US system of inequality exists, I suggest we work hard to automate, eliminate, and as quickly as possible banish labor for adults that won't secure them a reasonable living for them and their household. Educate, Train, and move them up the feeding chain to something more sustainable.
Twin studies suggest educational achievement is highly (over 50%) heritable. If you succeeded at replacing labor with education as a source of human dignity it would be surprising if the relative amount of dignity with which one was imparted did not depend on one's educational achievement. Combined with the first point it would lead to the formation of a kind of hereditary estates of the realm; you'd have the clergy (the academics), the nobles (the highly educated) and the commoners (everybody else). Would you find such an outcome acceptable? (Just to be clear, I mean this as a genuine, not rhetorical, question.)