I do not think that illegal immigration helps us. People like illegal immigrants because they "work for cheap" in many industries. Those people are taking services from Americans however. They are also sometimes taking jobs that Americans want. Not all jobs illegals have are the ones Americans won't touch.
You would think that this would be an easy question to answer one way or the other just by using numbers, but it is not. As you can see from the two links below, there are real disputes over the economic impacts of illegal immigration.
On the minus side, people argue that illegal immigrants take jobs from Americans and drive Americans' wages down in the process. Because illegals are willing to work for lower wages, they displace Americans in low skilled jobs and create a surplus of labor that makes all lower skilled workers' wages drop.
On the plus side, there are those who argue that illegal immigrants free Americans up to do better jobs. They argue that the immigrants take low-skilled jobs and Americans, who are better educated and trained, can then take jobs more in line with the kinds of skills and education they have. This enables our economy as a whole to get better and "smarter."
There is, however, no way to definitively prove which of these effects is bigger or more important and so this issue remains a controversial one.