Gary, I tried singing the Tennessee Ernie tune to the more elaborate chord progression, (Em, Em, C [or Am], B7, etc.).It can be done -- i.e., the chords do fit --, but that chord progression tends to make you want to change the tune to the one the Weavers sing.
Especially when doing it in a jam session, it seems to work better to apply "Ockham's Razor," as it were, and just use Em the chords you posted. In this case, "Keep [the chords] simple, sweetie, " seems to apply.
Genie