Whom I would like to invite to the party has not been decided.

不可以,这里whom是invite的宾语,只能用宾格
who在定语从句中只指人,作主语,也可以代替whom作宾语,例如：
Do you know the scientist who gave us a talk yesterday?
（指人,作主语,可用that代替）
The boy who broke the window is called Jim.
（指人,作主语,可用that代替）
This is the man (who) they were talking about just now.
（指人,作宾语,可用whom或that代替,也可以省略）