Does an iCloud backup recovery keep the original timestamp for a message?

Yes. Everything restored will reflect the status at the time the backup was made.

HOWEVER, if you sync texts to iCloud the text messages will not be in the backup, as the backup excludes any data that is synced. Thus, go to Settings/[your name]/iCloud and look at the switches. If Messages is ON then messages will not be in the backup, but will restore to the phone when you turn on Messages after restoring.

Go to Settings/(your name)/iCloud. Is the switch for Messages on or off?

Did you have iCloud message sync on or off? That is, did the messages restore from the backup or from iCloud Sync?

Then the backup contains no messages when you restore a backup.

For any iCloud sync, including messages, content you sync will be excluded from backups, to avoid doubling the amount of storage for each data type.