No, they will not work in menu versions of Word.

Word 3 was for the Macintosh in the early '90s. Word 2003 is Word 11. I know, it is arcane, stupid and confusing. Thank you MS marketing.

To use legacy form fields and protection for forms, any area you want people to type in has to be in a separate Section. Insert a continuous section break. Let Word know you do not want that section to be protected.
Sections / Headers and Footers in Microsoft Word 2007-2013
Using Forms in Microsoft Word

Alternatively, if the amount people have to write is not huge, you can insert a form text field that they can type in. A further refinement would be on-exit macros for your checkboxes that enable/disable the related text fields depending on the checked state of the checkbox. That depends on the people using your form enabling macros.