Yes, it is. Alkalinity, put another way, is a measure of the water's ability to withstand changes in pH, specifically due to the addition of an acid. That acid comes from fish and animal respiration (CO2 + H20 = H2CO3 or carbonic acid). A low alkalinity means that you could have high swings in pH...fatal swings.
In one case I encountered, there was a lady who really didn't mess much with her tank. She thought things were going fine and decided she wanted to add some more fish. Well, bammo, many of them died. The fish she had became acclimated over time to the decline, but the new fish pushed it over the edge. She added enough bioload, with a low enough alkalinity, that her pH crashed. So yes, it is an important measure, even without corals. Many fish only people watch pH and alkalinity, and not calcium.