Providing you've taken no log backups between the backups that got copied and the configuring of the mirror, yes it will catch up. If you have, all those log backups need to also be copied and restored on the mirror before you can start the mirroring.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability