There are four dataset classes which can be uploaded to GBIF. One is occurence data, which (probably) is fine to export from Specify, as is.And this is what you are referring to “include taxon information as part of the specimen record”.
However, another GBIF data class is Checklist data, which is what I was thinking about. This class does not require any specimen records.
In our Specify setup the Taxon tree is being used as our country checklist. Many of the taxa without any specimen record. So, is there any way of exporting the taxon tree or, preferably, a subset of it?