Depending on type of vnav operation, yes there are.
We have on the 737NG the requirement to disable VOR/DME updating when flying RNP-AR approaches, DME/DME doesn't have to be inhibited if DME/DME updating has been verified to be adequate. However for the rest of the operation there is no such limit.
However that is purely for lateral navigaiton accuracy, vertical navigation accuracy is displayed and checked differently and depends on baro information only, the default value is 400ft which has to be set to 125ft (for RNP-AR) if the airplane is equipped with navigation performance scales.
GPS height information is only used during GBAS approaches which are a completely different thing again.