display:none property makes your code behind that element not to execute. You can put code to write your rich text field in a server side javascript (on button click perhaps).

Your code for writing it down would be something like this:

var logDoc:NotesDocument = document1.getDocument(); //presuming document1 is the name of your datasource for form to which you want to save

var rtitem:NotesRichTextItem = logDoc.createRichTextItem("LogDocInfo"); //LogDocInfo is name of the RT field on your form

     rtitem.appendText("Server: ");
     rtitem.appendText(session.getUserName());
     rtitem.addNewLine(1);
     rtitem.appendText("Database:  ");
     rtitem.appendText(database.getFilePath());
     rtitem.addNewLine(1);

// append more stuff per your needs

logDoc.save(true, true);