from the paper, section 3.1

We train SBERT on the combination of the SNLI
(Bowman et al., 2015) and the Multi-Genre NLI dataset.

So yes, it’s trained on MNLI .
My guess is as it’s trained using Triplet loss to produce embeddings that are semantically meaningful
and can be compared with cosine-similarity, it might nor perform well on just classification .