Don't worry, if microsquish don't get their money you'll have plenty of problems with all of their products. (Wait a minute....)
But seriously, to my knowledge MS Project is a management control product based on building a Gannt chart for planning and controlling a project through the stages a project takes. You can schedule billing as a separate task to be executed at various times (particularly at the end) of the project. I do not think Project can fabricate a Word document to be sent or if it can just automatically print an appropriate existing Word document when the conditions for that task have been met.
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"Don't disturb my circles." translation of Archimedes last words