Well audiozen, Clapton and George Harrison were very close, so Eric may in fact have played on another White Album song. But he talked about how amazed he was that George invited him along to a session one day, and how "wrong" it felt to be playing on a Beatles record! It just so happened that they were recording ’WMGGW" that day, and aren’t we glad! Clapton never mentioned playing on any other of their songs, that I know of.
The guys he really wanted to play with were The Band. After hearing Music From Big Pink, he made a pilgrimage to Woodstock, waiting, he says, for them to ask him to join. After all, he disbanded Cream after hearing MFBP ;-). He says he finally realized they didn’t need him, and went looking for another good band to play with. He found one in Delaney & Bonnie’s road band, where he met the players who were to become his band in Derek & The Dominoes.