my understanding is this...
if the image is actually included in the email, without a link that is pulling the pic from serverB, then no, it's serverA doing the work, but if the pic is going to person1 in this fashion, then serverA does the work once, and if person1 forwards the pic 1000 times, it is person1's server doing the work 999 times, and if it is a pic pulled into email via a link to the image, then yes, serverB is doing the work. note that the image may be cached, so that is why it might still appear while offline.