So, your thought is that the increased metabolic demand of this 'TDS
creep' is going to place the fish in undue stress?
If that's the sum of it, I don't think you necessarily have much to worry about. Relative to the total metabolic demands of the fish, the expenditure of the fish's gills/kidneys (I believe most of the ion balance work is done by the gills in fish, may be confused on this point) is probably non-trivial, but ultimately not going to be a problem in a well-fed aquarium fish.
Second, it's important to note that the TDS
creep of most tanks is going to be slight, especially if you're just feeding fish. There are a few things that you can do to increase it faster, such as aquarium ferts, leeching rocks, water softeners, or non-DI
topoffs, but overall it's not going to be that much different in the long run.
I do see two fish health related consequences of TDS
though. The first is the classic 'old tank syndrome' that you sometimes hear about, wherein a tank that hasn't had it's water changed in months is suddenly cleaned (including a larger water change), and a bunch of fish die. This is likely due to TDS
/pH factors, as the tank had been topped off with tap water for months, slowly increasing it until it was significantly greater than the tap, then the sudden change in conditions when you replace most of the water with tap water causes an overload in the homeostatic mechanisms of the fish, leading to tissue damage or death. The other would be in classically soft water (or hard water) fish that are subjected to an increase in TDS
well beyond what they naturally would have experienced. In that case, their natural regulatory mechanisms might not be able to 'rev up' enough to meet these demands, resulting in their death as well.
Food for thought.