Hi Tammy,
Yes,
When I get a message about a new project in my inbox, I set the rule like you mentioned.
When a message arrives with project name in the subject line, move it to a folder with the same project name.
That part works well. But my sent messages don't end up in that folder.
I've tried making the same rule on my sent box. When I make the rule, there is a pop-up asking if I want it to apply to messages already in the sent box. I select yes and it works. But then it does not work for subsequent sent messages.