I think it varies from org to org, and it depends on the timing of the new member classes.
I was in a local sorority that went national. A couple of weeks after we pledged, a new girl joined us; as soon as she was pinned, she was considered to be on the same footing with the rest of us. She caught up to us in her new member education, and was initiated with us as part of the Alpha new member class. (This, BTW, is unusual - to be initiated while your "chapter" is still a colony.)
The following fall, we got an amazing Beta new member class. After they completed their new member program, they were initiated, and immediately afterward, we had our chapter installation ceremony.
There was some disagreement between us and nationals as to whether the Beta class would be considered founding sisters (we said yes, they said no). Ultimately, they were, but the compromise was that the signatures on our charter are in two columns - Alpha and Beta.
My apologies if I've confused you
