That's a true ad-lib.
The vanilla text is funny by itself, and a lot of it is indeed scripted, but the actors do a lot of their own flavoring of the text, either in minor one-liners or with interacting with the audience. The only "ad-libs" that aren't real are the hummus sandwich and the woman invited onstage.
The night I went, a woman in the audience (several rows back, mid-orchestra) offered a cup of wine- which James gladly took and drank.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."