Hello Linda. To answer your question directly, no, it does not strictly matter if you skip browning when you are in a rush. Your dinner will still turn out safe and fully cooked in the slow cooker.
However, your mum is technically right about the flavor. Browning the meat creates what is known as the Maillard reaction, which adds a deeper, richer, savory depth to the overall stew. If you skip this step to save time, the stew will taste a bit lighter and more like a simple boiled beef soup, but it will still be completely fine for a busy weeknight.
If you decide to skip browning today to save time, you can easily compensate for the lost depth by adding a tablespoon of tomato paste, a dash of Worcestershire sauce, or a good quality beef bouillon cube into your slow cooker liquid. This helps make up for the flavor you miss out on by not searing the meat first.