Yes, it seems that way. I've checked the dates and they are rock solid.
Also the song 'Let It Be' itself was close, issued as a single on 6 March in the UK - the Bud Shank album was reviewed 14 March in Billboard.
As most of us know, the 'Let It Be' album was recorded before 'Abbey Road' that appeared in Sept 1969. Interestingly, the original 'Long and Winding Road' could have been issued by Tom Jones, he declined the offer from Paul to make it his next single, but his company (Decca, AGAIN?) held on to 'Without Love', a single that charted early December 1969.
Obviously, Bud Shank had access to the then unissued January 1969 Beatles recordings.
I'm mentioning Jon baggish here, as he may have more to add...