Jonathan,
Yes, you can do this as part of your template by adding the generic risks within the Project and then saving as a template. Another option, that may be cleaner is that you can create a Custom Action at the Organizational level so it shows up in the Navigation Bar under Custom Actions. this Custom Action would allow you to create a new Project same as you can out of the box but you can add a field where you can populate a related risk. This will allow you to create the relation to the generic risk and create the Project in one step.
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