I haven't seen an answer to your question posted, I had out my copy of the
Life and Times of the Steam Packet yesterday the answer is yes.

Ben-my-Chree.

During the History of The IOM steam Packet company there have to date been 5
different Ben-my-Chree vessels.

ON the night of 2nd June, after completing 3 round trips, the Ben-my-Chree
was in collision with another vessel soon after leaving Folkstone for
Dunkirk, and this finished her involvement in the operation.