It is possible to convert Word content to HTML, and you are always highly encouraged to write the content as web content, because there are sometimes issues we simply accessing, and opening PDFs depending on the device they are using.
But to answer your question: no, as long as your PDF is accessible. I'd suggest putting it through something like the accessibility audit tool if you have Adobe Acrobat. If you don't, you might give content creators a simple check list, such as:
- does your image have alt text if needed? (consider a decision tree/flowchart, example)
- are your headings marked properly using the built-in styles?
- are your tables formatted correctly? also tables are not used for layout
You'll probably notice these are typical guidelines when writing web content, but also apply to documents (Word, pdf, etc.).
WCAG has a list of PDF Techniques that you also want to check, but generally if you make sure that everything is tagged/styled/marked properly in Word, it should save to PDF with the correct tags and such.