Yes, this is definitely possible.
Because hard disks are exceptionally slow compared to the rest of your computer, there is virtually always a delay between when a piece of software is told a write to a file is finished and that file actually gets physically written to the hard disk. This keeps slow disks from making it difficult to keep using the computer. But until this write finishes, the data may only exist in your computer's RAM.
There are mechanisms applications can use to ensure data has been written out to disk, but there is a significant performance cost to using them, so a low-level application like
tar will not use them and rely on a higher-level tool to ensure data integrity.
tar is not doing this for you, you can ensure that any pending writes have been flushed out to disk using the
sync command. Once that command returns, you can be sure that any disk writes that happened before running
sync have been successfully written to the hard disk.
Additionally, if you cleanly shut down your system, one of the last things that happens is that any pending writes are synced out. So in the case of power loss, data may not have been written out to the disk, but in the case of a clean shut down, everything should be.