Why would they want to, if they can't work or get benefits? It would be like going shopping with no money:') IMO we have to get really tough with employers, including the people that need baby sitters, maids and gardeners.
Oh, right - assuming by that time that there will not be under the table cash work available as all employers will be tied into using workers with the new ID's and could be fined for using non-documented workers.
Still - I don't see an end to the "cash" work. And, I just can't personally see that they are going to be willing to return. Hope there will be strong deportation procedures or exit strategies. This looks like a big problem area but at least we will know who they are and their background.