This is a question I've been wanting to find an answer to, until now completely unsuccessfully. This story examines studies that tracked results of illegal immigrants legalized under the Immigration Reform and Control Act of 1986 and examined them again in 1992. The main result is it found significant upward mobility once immigrants were made legal. This varied among groups, notably lower for Mexican immigrants but does show that you cannot simply expect immigrants to stay where they are on the income scale once legalized. I'd like to track down more recent data, how do they look 10 and 20 years out? How do their children look? Still, this is a good piece of data.
Though I still think that any immigration reform needs to acknowledge this is an economic problem and needs to be dealt with in that fashion instead of through policies not adapted to regulating labor markets.