No its not the same as any poor family.
#1. Illegal immigrants don't qualify for welfare and a lot of other government services, and avoid even some of the ones they do qualify for. Even stuff like police/court costs are used far less by them.
#2. Nearly all the immigrant families who come over are working families, so you can't compare them with the average citizen poor family which includes plenty of people who are unemployed, on welfare, on disability, elderly and retired, etc.
#3. The main cost they DO qualify for is education for their children, which you can't even fairly count as a cost because every study shows that education FAR more than pays for itself due to the benefit to the economy when those kids start working. It's unfair to count the costs of educating the kids before you've counted the benefits of those kids paying taxes on their income for the next 40-50 years.