Your Career Services office should be able to clear this up for you. Every firm I know of takes part-time students, but you won't be able to participate as a 2L for OCI until after your second year of part-time studies, whereas full-time students do OCI after just one year. This is so because 2L summer associate positions occur the summer before you would graduate from law school.
As for the NALP stuff, what the data means is that firms generally won't hire part-time summer associates, not that they won't hire part-time students. Thus, if you work full-time now and attend school part-time, you would have to quit your job (or take a leave of absence) to summer full-time with a firm.