Não
O Instituto Salem Witches não é um dos eleven escolas de bruxaria
É uma referência de brincadeira para uma organização do Reino Unido, como afirma a própria JK (2015):
"The Salem Witches' Institute isn't a school, but a joke on the Women's Institute in the UK."
- link
Além disso, no livro, os membros são descritos como:
"a group of middle-aged American witches [sitting] gossipping happily beneath a star-spangled banner stretched between their tents"
Então, eles claramente não são estudantes.
Quanto ao que é o Instituto da Mulher (e por extensão, o que podemos imaginar, o SWI faria diga que faz):
The Women's Institute (WI) was formed in 1915 to revitalise rural communities and encourage women to become more involved in producing food during the First World War. Since then the organisation's aims have broadened and the WI is now the largest voluntary women's organisation in the UK. The WI celebrated its centenary in 2015 and currently has almost 220,000 members in approximately 6,300 WIs.
The WI plays a unique role in providing women with educational opportunities and the chance to build new skills, to take part in a wide variety of activities and to campaign on issues that matter to them and their communities.