I assume a leaving member would have a share on the publishing rights on all music by the GNR partnership before his departure. This was speculated when Axl sold all of his publishing rights to Sanctuary Music Publishing in Jan 2005.
If this is the case would it be possible therefore that Sanctuarywill release something after a period of time, if Axl does not?
Sanctuary Music Publishing doesn't have a say in releasing albums. That's the record company's job. I understand they control the copyright license to the GNR catalogue on Axl's behalf, previously this was done by Warner Chappell. This means they can license previously published tracks to films, commercials, etc.