It is possible via a workflow rule for each field you want the data to populate. Let assume that the field API name is $C_Product.
1 .Set up a workflow rule on the Work Item level.
2. That would be triggered up when a record created/edited.
3. Evaluation criteria: isNew() || isChanged($C_Product)
4. Action Update field: Project.WorkItems.Product
5. Value $C_Product
Please let me know if it makes sense and that you got this to work. If you are still struggling I would suggest you join one of our Advanced Configuration Office Hours - http://www.clarizen.com/live-demo.html