Is this a borrowing from English? Would Gwnân nhw olchi'r llestri nawr not be more accurate?
Yes, I can see that it is an accurate literal translation of the English sentence. But the English sentence itself is deficient in that it omits some words which the hearers have to fill in for themselves. "They will do the dishes" really means "They will do (the washing of) the dishes" or more simply "They will wash the dishes". For somebody learning English who is completely unfamiliar with it, to "do" the dishes could be a bit of a puzzle.