Hi again....no, that is not correct.What about the Allpass filter, that might have Q=0 it passes all frequencies.
We should not forget that the quality factor Q is in reality defined with respect to the POLE POSITION and, therefore, should be called "POLE-Q Qp".
An allpass filter has poles AND zeros which are symmertrical to the pole distribution.
Hence, each pole pair has a certain Qp value (like lowpass filters). More than that, also the zeroes have associated quality factors Qz. In both cases, the Q-values are a measure for the nearness to the imaginary axis.
Here is the classical Allpass function (2nd-order):