I'm not sure it'd make much difference. From reading & skimming meta-analyses myself I've inferred that the main speedbumps with doing them are problems with raw data themselves or a lack of access to raw data. Whether the data were originally summarized using NHST/frequentist methods or Bayesian methods makes a lot less difference.

Edit to add: when I say "problems with raw data themselves" I don't necessarily mean erroneous data; a problem can be as mundane as the sample/dataset not meeting the meta-analyst's requirements (e.g. if the sample were unrepresentative, or the dataset didn't contain a set of additional moderator variables).