No way. If you’re here illegally, there should be no earning your citizenship at all. You should be barred for life.
Just like any crime, there are differing degrees to an offense. Some illegals are here for legitimate reasons, such as, they cannot obtain documentation due to circumstances that are difficult for them to overcome, such as finances, language skills, or fleeing from an oppressive government. For example, if I were a Mexican with a family to feed, I would probably try to get into America in order to have a better opportunity for my family. I don't see how you would compare someone like that to a career criminal who is just here to reek havoc and disobey our laws.
You must also remember that historically our immigration laws have not always been as strict as they are now, not that they cannot be improved upon; but if an illegal is here to assimilate, they should be given a chance to prove themselves and pay their dues to society before we ship them off. I certainly would not want to continue to overcrowd our prison system to the the degree we are now. You have to remember that every prisoner's incarceration is paid for in full by you and me the taxpayer. For some crimes that kind of economics is an unnecessary expense.