Rule-based functionality in Salesforce rarely allows you to assign things to users, even dynamic user values that are data-driven, for instance the user who is identified as the LastUpdate user or Owner.
There are two ways I could see you accomplishing what you are after, depending on what exactly the underlying goal is.
If you want to always be able to see the Account address information on the Contact, consider using a set of cross-object formula fields in Contact that simply reflect the current Account address info in that record. In this instance, no additional work on the part of the user required. The next time they look at the contact record, the address info will be updated.
If you really want a user to have a task assigned to them, or have some other way to virtually tap them on the shoulder and tell them to look at the contact record, too, you can do what you want with a relatively straightforward trigger. But once you are writing Apex, you have many more options for notifications: task, email, chatter post, UI message message, or just automatically just go to the contact record and update it.
So the answer to your question is, yes, it is possible. But you will need to decide which of these options best suits your requirements.
First of all, the feature Tasks to a Queue doesn't exist. But there is a highly voted on Idea that you should upvote
In the comments thread, there is a workaround that you could consider:
We added a role that reports up to the role(s) that respond to tasks,
and put a dummy Customer Service user into that role. New tasks are
assigned to this dummy user, and it acts as a queue. As a higher-up, a
customer service rep can reassign the tasks from the dummy user to
themselves, or if you are a manager, to others.
Alternately, you can
create sharing rules that explicitly grant access to the objects the
distributed tasks will be associated with. People are notified of
incoming activity/new tasks because the dummy user's email is set to
something like customer_service@mycompany.com. Folks on the email list
respond appropriately. You could also automate it with a workflow rule
that emails a specific group upon task creation. This requires a spare
license and of course, YMMV. Hope this is helpful!
-- James Snavely
Best Answer
Task's "Assigned To" is a lookup that can go to User or Calendar. Compare it with say Case Owner that says it can go to User or Queue. (that's your first issue, forget public groups, read about queues). Maybe you could make something happen with public calendars / calendar sharing. Haven't used them to be honest.
So the task can only ever get one owner. If you don't want duplicated tasks (and then some mass close / delete them whenever one user completes the work) not sure what else to suggest you...
How important is this work? Is it a show-stopper without which Opportunity can't proceed? Maybe you could just submit it for approval (with multiple approves set to "first come first served" or 1 approved Queue). With the setting "approver can edit the record even though it's locked" it could work quite well.