Is it possible to add to-do items using Siri on the apple watch? If not through a watch app, then would it work with an integration with the iOS Reminders?
Hi @bnicholson, welcome to the community! 
It’s not possible at the moment. You can add this as a suggestion using this form:
Maybe you can do something with Zapier https://zapier.com/blog/zapier-siri-shortcuts/