Of course immigration increases rental costs. If you increase the supply of available labor and demand for housing, wages will decrease and home rental/purchase prices increase.
Immigration also increases the size of the economy, so wages are not necessarily affected in direct proportion. There is the question of existing demand for labor (there may be a relative shortage) and where the labor goes/is needed. But as the economy grows more jobs are created, and the economy may become more productive.
If the economy is bad you'll get also emigration to some extent.
It could increases the size of the economy longer term but makes the average poorer. If there is an area of the economy with worker shortages it could increase production. But add immigration to a balanced job market and wages drop, employer profit increases (rich get richer) and the economy grows. Replacing workers with slaves increases the economy. Canada has encouraged mass migration and it has kept wages extremely low and has also increased the price of housing.
