If Fed buys more mortgage-backed securities, does it necessary mean that the interest rate will go down? Consider the supply and demand market for mortgages and let us assume the supply side is the commercial banks and the demand side is households. It follows that supply increases as Fed buys mortgage-backed securities, which causes the interest rate to fall. However, suppose that although the Fed starts buying mortgage-backed securities from the banks, the banks think it is too risky to hold mortgages after the increase in the delinquency rate during the financial crisis. So the supply does not actually increase and thus the interest rate does not increase. Is this scenario possible?
Addressing your question directly, yes, the rate will necessarily decrease. The Fed's purchases of MBS were entirely MBS that were securitized by the government-sponsored enterprises (GSEs). GSE MBS are not subject to credit risk, as the credit risk is guaranteed by the GSEs.
Further, banks underwriting mortgages that are securitized through this channel aren't holding any credit risk— the only real risk they face is that if a loan that defaults is found to have underwriting defects, the originating bank can be forced to repurchase the loan from the GSE through which it was securitized. This repurchase risk isn't trivial, but it can be controlled in a number of ways (proper underwriting being foremost among them). As a result, the channel that you posit— bank perceptions of mortgage risk increasing, offsetting rate decreases brought about by QE— is not possible.
Empirical evidence supports the above assertion— rates did in fact decrease. Krishnamurthy and Vissing-Jorgensen say:
We document that the Federal Reserve’s purchase of long-term Treasuries and other long-term bonds ("QE1" in 2008-2009 and "QE2" in 2010-2011) significantly lowered nominal interest rates on Treasuries, Agencies, corporate bonds, and mortgage-backed securities, but with magnitudes that differed across bonds, across maturities, and across QE1 and QE2.