Good question. Not sure of the answer but here is some info to consider.
As Bob Lusk often says if it can dissolve in water it will. Same for lime. Pond water always reflects the nature of the land it flows through/on. The reason most ponds are acid if they are is because the land/dirt they sit on/around is acid.
The undissolved lime will change the ph/alkalinity of the pond bottom/dirt just as it does for crop land or food plots for game.
Sodium carbonate (also known as washing soda or soda ash), Na2CO3 is a sodium salt of carbonic acid. It most commonly occurs as a crystalline heptahydrate, which readily effloresces to form a white powder, the monohydrate. Sodium carbonate is domestically well known for its everyday use as a water softener. It can be extracted from the ashes of many plants. It is synthetically produced in large quantities from salt (sodium chloride) and limestone in a process known as the Solvay process.
I know Na salt (soda ash) can be used in the pond sealing process. I am not enough of a chemist to know what other effects you might get from adding a sodium salt to the water or how long it aids alkalinity. I have never seen it suggested in the lake/pond mgt publications. I am fairly sure I would rather have the Ca than the Na in biologic processes.
SRAC -
https://srac.tamu.edu/index.cfm/event/getFactSheet/whichfactsheet/112/ Carbonates and bicarbonates are the most common and most important components of alkalinity.
Calcium and magnesium are essential in the biological processes of fish (bone and scale formation, blood clotting and other metabolic
reactions). Fish can absorb calcium and magnesium directly from the water or from food.
However, calcium is the most important environmental, divalent salt in fish culture water. The presence of free (ionic), calcium in culture
water helps reduce the loss of other salts (e.g., sodium and potassium) from fish body fluids (i.e., blood). Sodium and potassium
are the most important salts in fish blood and are critical for normal heart, nerve and muscle function.
Research has shown that environmental calcium is also required to re-absorb these lost salts. In low calcium water, fish can lose (leak)
substantial quantities of sodium and potassium into the water.
Ideally, an aquaculture pond should have a pH between 6.5 and 9 as well as moderate to high total
alkalinity (75 to 200, but not less than 20 mg/L) and a calcium hardness of 100 to 250 mg/L CaCO3.
Here is another source
http://www.ca.uky.edu/wkrec/LimingPondsAquaculture.htm