No. Non-admin users can't access other users directories and files stored under the home directories.
However, it is possible to circumvent users permissions. One example would be if someone were to boot from an install disk, target mode or external drive. Another would be someone savvy enough to gain root access after logging in as a standard user.
The easiest approach to ensure your users files are safeguarded would be to enable FileVault. On 10.4, it encrypts a users home directory only, not the entire disk like FileVault 2 does in later OS releases. But it’s better than nothing, and cheaper than a third party solution (if alternatives ever existed for the older versions).