Can AE Export a Quicktime Reference?
No. How should it? Ref movies are just what the name implies - basically playlists inside a MOV container referencing the original OMF/ MXF clips. No program other than Avid's own tools have a way of creating this, because it would require to be able to access the media database.
If not, what is the best way to send footage back into Avid Media Composer?
Set your QT CoDec to the Avid CoDec you are using anyway, then do a fast import. Otehrwise any otehr QT CoDec will do as well.