I could only speculate from what I hear about the level of connectivity in certain areas, but the alert system does also issue alerts over radio and TV, so it's a three-pronged approach. It helps, obviously, if your radio is on or your TV is on, so you'll still get alerts. That helps to cover more of the bases, regardless of the situation. However, you need an LTE connection to receive alerts otherwise.
On October 3rd, 2022. See this statement in context.