That depends on whether immigrant workers function as substitutes for native-born labor or complements to them:
The Economics of Immigration: A Story of Substitutes and Complements
"Immigrant workers can either be
substitutes for native-born workers or
complements to them.
"When immigrant workers are substitutes for native-born workers, they compete for similar jobs.
"Using a simple supply and demand model, an influx of substitutable workers constitutes an increase in the supply of labor, causing wages to fall for workers with similar skills..."
"However, when workers are complementary, an increase in immigrant labor can increase job opportunities and wages for native-born workers.
"So, the low-skilled immigrant labor reduces the cost of production and increases the output of those goods; this greater output increases the demand for other, higher-skilled workers."