The absence of an observation may be strong evidence of absence or very weak evidence of absence, depending on how likely the cause is to produce the observation.
So, yes, absence of evidence can convincingly disprove a theory in some cases (although, as ChristianKI points out, Bayesians typically do not assign probabilities of 0 or 1 to any theory).
From the OP:
So, yes, absence of evidence can convincingly disprove a theory in some cases (although, as ChristianKI points out, Bayesians typically do not assign probabilities of 0 or 1 to any theory).