"Are you well, Andreas?"
Obviously this で doesn't prevent me from understanding the sentence. However, what does it add to the sentence?
This で is a sort of situation/method/means marker, and the sentence is confirming アンドレアスさん is the right name, choice, etc. "Is it okay if I used Andreas-san?" is a terrible translation but should help you understand the gist of the sentence.
For example, this is used in the following situations.