Absolutely. And if the project goes as planned, please do so too! The is no way I can imagine where we create the complete Strategy upfront and we stick to it until the end. Also look at my answer for question 9. I think a Test Strategy should evolve from small and general to big and detailed over the curse of the “test project”.
For me a Test Strategy is an evolutionary (mental) model that changes all the time. When I learn new things, when I get new insights, when I see parts of it aren’t working as planned, when I get feedback that the ideas I have aren’t effective or my way of working is inefficient. I share my thoughts and (parts of) my test strategy constantly with many people I talk to or work with. They help me sharpen my ideas.