That made me nervous!
I don't know enough about how Docker implements volumes under the hood to know how likely (or not) it is to break filesystem behavior that SQLite depends on for its transactional guarantees.
Perhaps someone here does?
What you should worry about though is the underlying volume driver and its storage type. Volumes can be simple bind mounts to your local disk, being more or less identical to no container. But volumes can also be attached straight to a network disk, where same dangers apply as if you would have mounted that network disk on host.
Volumes are made exactly for holding databases. And also bind mounts should work without any issue in most configurations.
But if there is some kind of network/virtualization between the physical disk and the container, you should investigate it in more detail.