At a top 10 school (are there ones that are not well-regarded?), even if you are in the bottom 20%, you will have a good shot at biglaw. You will get an additional boost if your school does not allow firms to pre-screen candidates. My friend had a great strategy to counteract her low GPA. When she walked into the interview she did not immediately hand the interviewer her resume. Instead, she wowed him or her with her personality and only provided the resume on her way out. She got two offers at V10 firms and many others at other firms with grades below the median. If your school does pre-screen, it may be more difficult to get interviews so just apply to a wide range of schools to hedge your bets. And don't listen to mutual_biscuit (assuming he or she is not joking), he or she clearly goes to a TTT. Practically everyone at top 10 schools is able to secure law firm employment if they so desire.
The OP specifically said that he (or she) is "friendly and socially extroverted" and I will take the OP at his (or her) word. Moreover, the strategy could only offend an employer if the interviewee refused to provide his or her resume upon request (which would clearly be stupid and unprofessional). Not all interviewers immediately ask for a resume (many of mine did not). Consider the converse: "an average law school nerd" in the top 10% of his class at a top 10 school arrives at an interview and immediately presents his resume to the interviewer because the nerd is terrible at interviewing but knows that once the interviewer sees his class rank, a callback will be more likely forthcoming. Is that similarly disingenuous? Both the nerd and someone who uses the strategy are simply playing to their strengths.