I think integrating Stack Overflow with LinkedIn by showing Stack Overflow application in the LinkedIn profile will help increase the attractiveness of a profile.
By just showing Stack Overflow reputation points in the LinkedIn profile it would add value to the profile/resume. For a recruiter this number will mean one more parameter to shortlist, as Stack Overflow reputation point tells about how much a person's solutions, answers and thinking is appreciated by others, his/her technical knowledge and his/her ability to explain, communicate, and convince.
Is there an application already or in development? I did look around a little bit and didn't see any open SDK to develop such application on my own, though I see LinkedIn provide some APIs. Is there something in the pipeline?