"They toured The White Album?"Well, the 'White' album was released Nov. 1968. The Beatles played on the 'Roof Top', Jan. 1969. Unfortunately, this 'impending' tour was curtailed halfway through 'Get Back'.
It not very well known, but according to the set-list taped on 'the BASS', the next song, following 'Get Back', would've been 'Back in the U.S.S.R', followed by 'Dear Prudence' and so on...
So following this logic, yes, the Beatles were intending on touring in support of the 'White' album.
Interestingly, McCartney's 'other' Hofner (his first one, Cavern Bass) was stolen during the filming of 'Let It Be'. It is the one he played in the 'Revolution' video, and probably on the track. It still has not surfaced. McCartney played 'the BASS' during the 'Roof Top' concert.