Adding pure Cyanuric Acid (CYA) does not change the Total Alkalinity (TA) because the lowering of pH and TA of the weak acid (hydrogen ion) counteracts the rise of TA from the salt (cyanurate ion). However, liquid CYA is sodium cyanurate so increases the TA where for every 10 ppm CYA the TA is increased by 3.88 ppm so James' second calculation is correct.
Note that this rise in TA is not due to carbonate alkalinity so is not increasing the rate of carbon dioxide outgassing and is not changing the Calcite Saturation Index (CSI) so is not something someone should worry about or adjust lower if your water chemistry was already in balance and you were just increasing the CYA level.
When you add pure CYA, however, the TA doesn't change upon addition, but the pH is lowered (so carbonate alkalinity is lowered) so depending on how you raise the pH you can affect the CSI. If you let the pH rise from carbon dioxide outgassing, then your CSI will drop relative to where you started, essentially because you've added an acid and aerated (allowed outgassing). In an extreme situation adding 80 ppm pure CYA and having carbon dioxide outgassing bring the pH back to where it was before you added the CYA, the TA doesn't change, but the carbonate alkalinity (at pH 7.5) drops by 24.8 ppm and the CSI drops by 0.16 units. So not a large amount, but not insignificant either.