Adding carbonate will indeed stabilize the pH. Carbonate is one of the most common buffers of pH in aquariums. If you had low or variable KH, then the pH could also be variable. By dosing just a bit of carbonates, to maintain a stable value for the carbonates the pH is much more likely to be stable.
The pH may not test the exact same value through the day, but will probably follow a cycle of higher in the afternoon and lower in the early morning.