It's kind of like an elision where the end of one phrase is the beginning of the next phrase. The verb is elide.
In music elision is specifically about the notes overlapping in phrases. But, there is a general meaning for elision as some kind of overlapping or omission.
This may not be the correct usage for elision, but it's the word that came immediately ...
The term would not be "descant"
The term you and your director are looking for is "vocable"
We use the term "vocable" to describe sounds singers make that are outside of intelligible language. Beyond "oohs" and "aahs" it would also include whoops, screams, pops, clicks, lip buzzes and any of the other thousands of sounds the human voice can make.