Yep, waltz up with a resume and be prepared to chat with them and request an interview.
I actually helped to run a hospitality suite once. From the lawyer/recruiting personnel's point of view, you'll see a lot of strangers walking up. Some strangers are on the interview list and some are strangers who want to be on the interview list. It's actually really helpful if you clarify your intentions quickly.
Yes, it's an awkward kabuki, but firms run hospitality suites to give more info and potentially pick up extra interviewees. Many firms really bend over backward to pencil in extra people during scheduled breaks or even once the day is over.
A perfectly acceptable strategy would be to introduce yourself as hoping for an interview, offer a copy of your resume, and then stay to ask a few questions about the firm before moving on. That part is a little awkward but should be straightforward - the hardest part is that you might get to the hospitality suite when the people from the firm are already surrounded by a few other law students, making it hard to do anything initially but saunter up and listen. Just remember that the people from the firm can't try to get you an interview until they know you want one. Be polite and personable and don't take it personally if you can't fit in everywhere.
Penn doesn't let us calculate a GPA or put one on a resume. We hand them a transcript when we sit down at the interview table. Should I hand them a transcript and a resume? No cover letter, oui?
Penn 3L here, when I did this last year I handed them my transcript and resume when I was requesting an interview with a firm I didn't have scheduled. At this point CPP can't do anything to stop you from showing them your grades, and I think they want to see your transcript to decide whether they want to try to squeeze you in or not.
I think the best strategy for doing this is to show up first thing in the morning, about 30 minutes before the interviews are scheduled to start and find one of the attorneys doing interviews (sometimes this will be obvious since they will be sitting in the interview rooms, if you can't figure out who is doing the interviews, then give them to someone in the interview suite who looks authoritative/in charge/older, not necessarily an attorney, handing it to the recruiting person can be better in some instances than handing it to a junior associate who is staffing the hospitality suite all day because the recruiter will be organizing things and might have more control over the interviewers schedules). I did this several times last year and after handing the attorney my resume and transcript and explaining that I was really interested in the firm for X reason but didn't get an interview in the lottery they often offered to interview me on the spot before their schedule for the day started. This requires getting up and being at the interview suite really early, but if its a firm that you really want to interview with I think it is way better than going later in the day.... they actually have time to interview you, no one else has beaten you to the punch and taken their breaks or scheduled interviews for the end of the day, you can get to the actual interviewers instead of only people in the suite, it shows that you wanted it badly enough to come early, and there aren't as many other students around the hospitality suite so you don't have to stand around forever waiting for a break in conversation or a chance to talk to someone.