Does NY State have the right to declare an illegal immigrant a citizen of that state?

[KittyWampus]

Or to at least issue some kind of documentation to said illegal immigrant. Something that would enable NY to deal with said illegal immigrants?

In other words, since the federal system isn't stepping up to the plate, can NY or any other state do the paperwork. At least for that state alone?

Is there some way for NY to issue documents to illegal immigrants just to get them in the system?

Edit- I'm trying to find ways around the drivers liscense for illegal immigrants dilemma.