No. Harvest Moon: Back to Nature released exclusively on PlayStation 1 (1999/2000) and later ported to Game Boy Advance as Harvest Moon: Friends of Mineral Town (heavily modified).
It was not released on PlayStation 2.
Actual PS2 Harvest Moon Titles
Harvest Moon: Save the Homeland (2001/2002) — First on PS2, different gameplay (no marriage)
Harvest Moon: A Wonderful Life (2003/2004) — Also on GameCube
Harvest Moon: Another Wonderful Life (2004/2005) — Female protagonist version
Harvest Moon: Magical Melody (2005/2006) — Port of GC game
Modern "Back to Nature" Experience
GBA: Friends of Mineral Town (via NSO/Emulation)
2019 Remake:Story of Seasons: Friends of Mineral Town on Switch/PC/PS4/Xbox
