It wastes it if the category is complete, but that level is still open.
Yes, it’s absolutely worth organizing your alliance to have one person open their rewards and report back what can be done to further the mission without wasting resources.
If collect DNA and collect rare DNA are complete, but the other categories in that level are not complete, any DNA collected is not counted towards the alliance missions…
The faster you can complete the first few levels, the less wasted resources, the faster the next missions are complete.
It’s NOT an easy process, and requires your alliance to communicate well.
Best of luck to you and your alliance!