The conventional wisdom is that you can't do this just using field codes, and the simplest workaround using that particular type of field code (legacy non-ActiveX FORM fields) is to use a drop down form field with (say) Yes and No options. If the dropdown's bookmark is Dropdown1, then you can use something like
{ IF { Dropdown1 } = "Yes" "some text" "some other text" }
I believe that is actually the safest way to go using that generation of form field.
OTOH you might be able to get away with this, although I suspect that even if you can get it to work, problems outweigh any convenience factor involved.
Say your document's path is c:\a\mydoc.docx, and your Checkbox bookmark name is CHeck1, then insert the following LINK field:
{ LINK Word.Document.12 "C:\\a\\mydoc.docx Check1 \a \t \#"'checked';;'unchecked'" }
Enable protection for forms in the usual way, then check/uncheck the box.
Here, the LINK field does update, but after a short pause.
LINK fields can also be hard to maintain because you have to have an absolute path to the document, and that will change if you move the document.
Something similar appears to work on the Mac version of Word, except that you cannot use the # numeric format field, and you have to use an IF field instead, e.g. something more like
{ IF { LINK Word.Document.12 "/Users/username/a/mydoc.docx" Check1 \a \t } = 1 "checked" "unchecked" }
but you can't use that on Windows Word because it doesn't update automatically!