This setting is nothing to do with the database transaction logs. If you have turned off circular logging (and you should, on production mailbox servers), the transaction logs are only deleted after a successful online backup of the information store. An online backup needs an Exchange-aware backup program, or you can use the regular windows backup (which is patched to become Exchange-aware when you install Exchange on the server). Online backups are the only way to regularly check for database corruption, ideally you should be doing one every night.
The setting "Don't permanently delete items until the store has been backed up" is part of the Deleted Item Retention period settings (otherwise known as the Dumpster). If you set a retention period, items that are deleted from mailboxes by users aren't really deleted, they're moved into a 'deleted items' area, where they stay for the time period specified. During this time period, users can recover the deleted items via this option in Outlook. After the deleted item retention period has expired for an item, it is normally purged from the dumpster by the overnight database maintenance.
Ticking this box means that the removal of the item from the dumpster will be delayed until a successful online backup has been taken of the store, even if this means that the item is retained long after the deleted item retention period has expired for this item. It's another level of safeguard, to ensure deleted items are backed up before really and truly being deleted. To make use of it you would have to be very strict about your online backup cycle and tape retention - for most people, this setting is probably overkill.