No ^^ Your source says the chewing ice is a known symptom of anemia, but does not say how prevalent this symptom is in anemia-affected people.

So from that source you can't conclude that anemia "often" leads to chewing ice, it may very well be quite rare.

Abstractly, "A is often a consequence B" does not logically goes to "B often leads to A".

To use an extreme exemple, crossing paths with polar bears (chewing ice) is generally linked with dieing (anemia), but death is quite rarely caused by crossing paths with polar bears.