Yes - the majority of the county (especially concerning where people LIVE) feeds into the high school. Thus why it is named Warsaw Community High School.
As well, while the town of Warsaw has a population of around 15,500 - there are MANY neighborhoods that are just outside of the "city" limits. My old home growing up being one of those. Also, it's important to remember that while Winona Lake is technically a separate town, the two are connected as one. Winona Lake has a population of around 5,000 itself. I would guess that the "greater" Warsaw area has at least 30,000 if not more population considering the county itself has about 80,000.
In the below screenshot:
Orange - Warsaw Community Schools
Green - Wawasee Community School Corporation
Pink - Wa-Nee Community Schools (NorthWood)
Blue - Triton School Corporation
Yellow - Tippecanoe Valley School Corporation
Purple - Whitko Community School Corporation