According to others (I haven't tried it), polysorbate 80 works well to pre-treat greasy spots on fabric and also works for cleaning hair, so yes it can cut grease. I think people are using PS80 undiluted for these purposes.
I'm sure PS80 would blend with a diluted liquid soap, so that's a feasible thing too.
But, like the others, I'm not sure how much grease cutting power it would add if mixed into a dishwashing soap. I think I'd use a more powerful syndet instead. There's a thread here on making solid dishwashing soap that's syndet based -- might be worth a look to see what detergents this type of product uses.
I also doubt PS80 will improve the lather of a liquid soap, if abundant suds is important to you.
Really the only way to know for sure is to make up a sample and compare the base soap with the mixture of soap and PS80.