this is a hard question. i'd love to say "yes" immediately, but then i thought, what if my beloved fell off the balcony (i'm on the top floor)? i know i will not jump off the balcony after him, but i will rush downstairs immediately. but this might be too late to save him.
i think it is more truthful for me to say i will do my very, very best to save my cat, even rushing after him into the middle of the road, or fighting with a bully who hurt him, or going into dangerous places to rescue him, but there may be situations like the falling off balcony where i know i will be too scared to reach out for him.
this has always been my biggest fear, actually, that he might fall off and i won't be brave enough to jump and grab him.