yes, it was recorded in Abbey Road alone on his guitar on 25th Feb 1969, his birthday.
he recorded two more demo's, All Things Must Pass & Old Brown Shoe on the same very
day, & they all appear on Anthology 3!
Harrison said that "I had a break while Paul was doing some overdubbing so I went into an empty studio and began to write. That's really all there is to it, except the middle took some time to sort out. It didn't go on the White Album because we'd already finished all the tracks." A demo recording of the song by Harrison from this period appears on the Beatles Anthology 3 collection, released in 1996.