Yes you can add a hidden field in an Embed Code component in the form, filled with the CMS value.
This one pre-fills a hidden field with the current page URL: Form in a collection page template- How to identify the page or item?
You can also do something like this, just replace [CMSVALUE] with a selected value from the CMS using the purple + link in the Embed Code component.
<input type="hidden" value="[CMSVALUE]" />