So... is Yoshinaga-sanchi no Gargoyle finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 25, 2006
Manga finished: July 15, 2008
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Yoshinaga-sanchi no Gargoyle centers around the Yoshinaga family, whose ordinary lives take a decidedly bizarre turn.
The catalyst for this change is Futaba Yoshinaga, who wins a seemingly innocuous prize in a lottery: a stone gargoyle.
However, this is no ordinary garden ornament; the gargoyle is actually alive!
The anime then explores the comedic and likely chaotic situations that arise as the Yoshinaga family adjusts to living with this unexpected, magical houseguest.