I don't think so. With a library-enabled content  type, you are
(essentially) already viewing the attachment. Essentially the opposite
of a list item.

Can you add attachment  fields to an Item content  type?

The only way that I know of would be to create a custom  field type  that
will hold a serialized file  stream as data. Although doable, it
wouldn't plug in to the builtin menus and controls for editing like the
existing document  field, so I don't think it would be of much help.

I'm a little confused about
what the UI would be like for the custom  field type
you mentioned. I only need it to function like the
attachments column on a custom list. I don't need any
of the check-in/check-out stuff.

Is this possible?

Yes, It should be possible. The UI would be to present a text box with
a Browse button in place of the field  when in Edit mode and to display a
descriptive title or the first few lines when in display mode. It would
require quite a bit of work, but should be possible. It would not
provide you with the Attachment toolbar button in the custom  list.