Almost right but not quite. 20 Mule team Borax can and does serve two functions in your pool.I consider Borax the icing on the cake.
1. The most important one is to use it to raise pH. It will do so with relatively little movement of the TA.
2. Secondly, it can be used (lots of it) to introduce borates to your pool as sort of a conditioner/algae preventative. Of course, it still raises pH so a lot of muriatic acid has to be used along with the 20 mule team to counteract that pH rise. That's the function that is "icing on the cake" and not at all required for pool water management.