Technically it's a translated song from the original english Country Road song, but yes the lyrics goes parallel with the one you mentioned sung by Youko Honna. (Sources from MyAnimeList.net)
From Wikipedia:"The songs were actually translated by producer Toshio Suzuki's daughter Mamiko with Hayao Miyazaki writing supplemental lyrics."So there :-)
Take Me Home, Country Roads - John Denver (Cover by Navaka)
Singer/Songwriter/Guitarist www.navakafernando.com Written by - John Denver, Bill Danoff, Taffy Nivert.
Take Me Home,Country Roads 4 29 73~John Denver with Bill&Taffy
LIVE performance audio Bill Danoff is 1 of the most under rated/under appreciated singer/songwriters in the universe"The Potter's Wheel"Afternoon Delight"Take ...
this cool...if you watch the video from the BBC show...you can tell they
doctored the audio from a recording and didn't use the actual LIVE
version...this is raw and rare..thanks for sharing