Yes, they will send your transcripts (but it doesn't show up it you click to view your academic summary report). However, some schools require that you send transcripts directly to the admissions office. It is probably faster to have your current law school send transcripts to each school directly. If you have the transcripts sent to LSAC it usually takes them a little while to process it and then they send it, and the schools request a paper copy which takes about a week or so to get there.
So, it is probably much better to have your law school send them out (even if your school charges you for each). That way, they will be there in just a few days after your law school mails them.