Yes. Immigration, as with many policies, has effects on both supply and demand. We note that in the monetary policy report.
Immigration will increase the labour supply, and that's a good thing. It will help relieve the tightness in the labour market. It also helps increase potential over the long term, but it is also the case in immigration that immigrants buy houses, as you note. They add to demand, so in an economy that's already in excess demand, adding immigration will add to both sides. It doesn't necessarily relieve the excess demand. It will add both supply and demand pressures.