Is it possible to hide a field on a form without writing code?
If you simply want to hide the field and have the default value saved, you should be able to simply hide the field with CSS. Find the ID of the wrapper surrounding the field and set it to display: none;.  Here is a working example from my D6 site:

#edit-field-vendor-sort-order-0-value-wrapper {
  display: none;
}