No, I don't see him on the listing I have - but that is not all that uncommon, either. Some of my own relations are there but not included in this record. One story I heard was that a previous person responsible for the cemetery decided that all that old set of records wasn't needed and threw them out - so there are a number of people buried there that don't show on the records any more.
Looks to be your James Riley Barfield is related into the Tillerys and maybe some Alfords (I think *everyone* in Waller Co is related into the Alfords!). There are a couple of unmarked plots there - but *on the records I have* (there are other, maybe even more 'official' records...) he isn't listed specifically.
Hope you can find some documentation! Maybe a newspaper reference to confirm the burial there?