I think it would generally inflate housing prices. The Fed is a large buyer that can 'print' its own money to purchase these assets, so there isn't much incentive for it to examine the debt that its buying. It buys these mortgage bonds from banks that may also be incentivized not to scrutinize the people they're loaning money to (beyond whatever is required by law in underwriting a mortgage), because they know the Fed will purchase their debt without much question.

Of course, there might be other reasons and counterarguments, this is just my interpretation.