This link from Microsoft explains a bit about transaction logs in Exchange 2003.
You are talking about 2 different things that are confusing you I think. The archive bit just tracks changed files during an external backup of the filesystem. Committed transactions are for the Exchange database to reference in the event of an unexpected shutdown. Transactions are first written to the transaction log and then committed to the Exchange database. The checkpoint file keeps track of which transaction logs have been committed to the Exchange database so if you had to to a restore of Exchange, it would know which transactions it has to restore from the transaction logs and which are already committed to the database.
This link explains a bit about the Exchange Backup procedures.
Performing a full backup physically clears the transaction log files from disk among other things, but is unrelated to the archive bit on the physical transaction logs. Here is an excerpt from the link:
The high-level interaction between the VSS, the Exchange writer, and Exchange Server 2003 during backup or restore operations is as follows:
1. The backup program (or agent) runs a scheduled job.
2. The VSS requestor in the backup/restore application sends a command to the VSS to take a shadow copy of the selected Exchange Server 2003 storage groups.
3. The VSS communicates with the Exchange writer to prepare for a snapshot backup. Exchange Server 2003 prohibits administrative actions against the storage group, checks volume dependencies, and suspends all write operations to database and transaction log files while allowing read-only access.
4. The VSS communicates with the appropriate storage provider to create a shadow copy of the storage volume that contains the Exchange Server 2003 storage group.
5. The VSS releases Exchange Server 2003 to resume ordinary operations.
6. The VSS requestor verifies the integrity of the backup set prior to signaling the backup was successful. Exchange Server 2003 truncates the transaction logs and records the time of the last backup for the database.
Here's one more link explaining the Exchange database and how transactions are processed.
You will probably get more out of reading the info in the links than you will trying to follow my horrible, convoluted explanation :)