CO2 injection needs to be handled carefully in any planted tank. Elevated levels can stress and eventually kill fish. Stress symptoms include lower activity levels or hiding, more severe symptoms include hanging out at the surface or high flow areas persistently, with the most severe symptoms manifest as fish swimming just below the water line with slowed reaction to stimuli. CO2 levels take time to build up - so it is always avoidable if you spend time observing the tank when CO2 levels are being tuned. However, many folks underestimate how long CO2 levels can take to build up - it can be as long as 4 or 5 hours for certain setups before CO2 saturation reaches peak rates.
CO2 tolerance also vary among fish and shrimp species. Discus are more sensitive to high CO2 levels compared to say, common tetra species. Caridina shrimp is more affected by it than Neocaridinas.
That being said, CO2 injection is very easy to handle safely if done well. This is especially so for tanks that are setup to have good gaseous exchange from the start (read the separate post on this). Having good gaseous exchange gives a lot of leeway for injecting CO2 vigorously.
There is a widespread concern that the pH swings from CO2 injection may hurt livestock. This subject is actually more complicated than it looks. It may or may not matter in your tank.
The main reason why pH stability is often quoted as important in aquariums is that pH levels normally reflect alkalinity (KH levels/carbonate hardness) which affects fish/livestock osmoregulation. Sensitive shrimp for example, are affected by sudden changes in carbonate salt concentrations in water and dislike KH swings of more than 3 degrees in a short time span. (This would be also reflected in the pH changing rapidly in a short time).
It is KH flux, not pH that affects fish and livestock heavily. However, in most tanks it is easier to get a pH reading than to test for KH, and pH readings has become the proxy for folks to estimate whether their KH is stable or not.
However, if pH is changed without a change in KH, as in the case of CO2 injection, the swings in pH generally do not impact livestock. Weak acids such as those produced by dissolved CO2 do not move KH much, there is no change in dissolved salt concentrations in the water column and therefore no significant impact to livestock osmoregulation from that angle.
Excessive levels of CO2, and extreme levels of pH ( where the acidity itself becomes an issue ) will still affect livestock, but these are separate issues from pH swings caused by CO2 per se.
Neocaridina shrimps breed and thrive in many CO2 injected planted tank setups where the daily pH swings are more than 1 degree.
Demonstrate of pH swings that have no impact on livestock
If we do large 60-80% water changes in our CO2 injected planted tanks, the pH changes a full 1.0 unit in 20-30 minutes or less, yet we never lose sensitive shrimp or fish if the other parameters are kept consistent.
pH swings ( 1 full point + ) also occur in nature very commonly, as CO2 levels build up overnight due to decomposition, but are quickly depleted during light hours.
Fish from acid peat swamps will do alright in a tank where the pH drops from 7 to 5.8 during CO2 injection as the low point in the cycle (pH 5.8) is within range of their natural living conditions. However, alkaline water fishes may not take the dip into the pH 5.8 range well. It is not the swing, but the pH value itself being outside of the fish's natural range. The same alkaline water fish can survive a comparative pH swing from 8.5 to 7. It is important to differentiate the impact of a pH change vs the impact of an extreme pH value in itself.
Head here to learn more on how the different water parameters affect fish.
The short answer is no. Bacteria colonies adapt to such levels. Thousands of aquasoil tanks with low KH have low pH levels of 5+ to 6+. Nonetheless they have no issue with regards to both livestock and plants. Read this article on how bacteria adapts to low pH environments.