Is it possible to make only one field in a content type language neutral?
I don't believe that it's possible to configure the language type of fields and translate per field. Not in Drupal 6 anyways.

This shouldn't be a problem anyways. When you translate a node, drupal makes a copy of the original node, which means the e-mail address will be pre filled with the correct value.

The does require some extra work when editing, but if you really wanted to, you could create some custom code, or maybe setup a rule, to keep that field in sync with the other translated nodes.