Sure; that is one way of interpreting those quotes. I tend to think of the cessation of existence as the mere cessation of ignorance regarding “existence”, but I do not claim to know Sariputta’s mind when he uttered those inspired and for me figurative words.
We don’t actually know where on the Dhamma path Sariputta was when he uttered those words do we? They were nor verified by the Teacher afaik.
The Teacher himself said on numerous occasions that just before the realization of nibbana occurs one does not make a choice to either continue existence nor to cease existence. Curious isn’t it? 