If you could carefully regulate the Trichlor, then you could set a TA where the rate of pH rise balances the pH drop from Trichlor acidity, but as Jason noted when the spa is used and the jets are running the pH will tend to go up quite a bit. The main way that is combatted is with a lower TA but that then reduces the amount of buffering against a drop in pH which the Trichlor will tend to do. So it increases your risk if you don't maintain that TA regularly. It's technically doable, but is regular maintenance not suitable to a service that doesn't visit very often.
Also, for Trichlor it dissolves more quickly in hot water so needs a special feeder that can be dialed way down, more so than required for bromine tabs that dissolve more slowly.
Remember that with Trichlor, for every 10 ppm Free Chlorine (FC) it also increases Cyanuric Acid (CYA) by 6 ppm and when the chlorine gets used/consumed, it also lowers the Total Alkalinity (TA) by 7 ppm. In a pool this is managed by a somewhat higher TA level and addition of pH Up (sodium carbonate), but in a spa with its low water volume, relatively high bather load, and sporadic aeration from jets, it can be harder to manage.