Technically the answer is yes. On the other hand if it's infrequently used it's probably not that much of a risk. I have baths that have no backsplash and haven't for years. They aren't used too much. The main problem is that the paint doesn't hold up that well over time. But if you use it a lot you should have a backsplash.

Is it a full bath or a powder room? A pedestal sink in a powder room is generally just fine without a splash. If a storage vanity in a powder room? Better looking with a riser splash matching the counter top.

If a full use, twice a day full bath.......yes a splash is probably necessary and advisable.