Hmm, good question. There is generally expected to be plenty of decomposition (or in biogeochemical speak "remineralization") happening any time you have enough

Hmm, good question. There is generally expected to be plenty of decomposition (or in biogeochemical speak "remineralization") happening any time you have enough organic carbon around (and enough of a chemical potential gradient between that and some oxidant) for somebody to make a living respiring that organic carbon. And just in terms of biogeochemical cycling the result is pretty similar whether the decomposition is being done by heterotrophic bacteria and archaea, or by fungi -- so to first order it wouldn't change that. Nonetheless, there might be some unexpected consequences if a significant proportion of the remineralization was being done by fungi.