Although I agree that the question is worded oddly, I can answer this one personally for Alpha Delta Pi
Legacy family members are absolutely invited to initiation, even when they technically would not be considered a "legacy" under our legacy policy: my chapter has aunts and cousins come and surprise their family members during the ceremony. I've told the story before so I won't repeat it, but my mom surprising me during my own initiation was one of the most moving moments of my life. Our pledging ceremony is fairly short, on the other hand, and I've never seen alumni invited to that.
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