They'll get applied. When restoring a database, you generally start with the latest full + differential then move onto the transaction logs. However, it is entirely possible to start your restore process from an older full backup then apply all the transaction logs to roll it forward. Slow way of doing things, but I have read stories of where it had to be done (due to more recent full backups being corrupted - fortunately they had an unbroken chain of log backups from that full backup up to current day).

Your full backup is the state of a database at a point in time (the time when the backup finished). The transaction log backups are a record of what happened to the database over a period of time.