Not exactly correct.
While some do pay taxes, many others do not. It is estimated that illegal aliens only pay about $11 - $12 billion a year in taxes. This is a small amount when compared to the estimated cost of illegal aliens which is somewhere around $100 to $195 billion a year.
As for getting benefits, this also is incorrect. They get medical benefits when they go to an ER and can't pay, their children get free education, free meals in school, etc.
If they have a child born in the U.S. they then also qualify for Medicaid, food stamps, etc.