Even during the worst parts of my months-long Ostreopsis bloom, I never had any issues with any of my fish, even the herbivores. So I wouldn't worry about adding new fish, and in fact having a higher bio-load will naturally increase nutrient levels and thus help prevent against dino blooms in the first place. However, if you are spending your time and effort dealing with the dinos maybe that isn't the best time to be selecting new fish and quarantining them or whatever your protocol is.
Corals are another story. Corals want stability, which is hard to maintain in a dino bloom as you are trying all sorts of different things to kill the dinos. Corals want >0 nutrient levels, which are hard to maintain when dinos are sucking up all the nutrients. Corals can also just physically get killed by strands of dinos attaching to them and directly killing the tissue.
For the microflora and microfauna that inhabit your tank, dinos also wipe them out in a different way. Dinos are very good at outcompeting other microalgaes at low nutrient levels, and since basically nothing eats dinos, their presence means nutrients are going to an organism that isn't going up the food chain. So pods basically have nothing to eat and their population will decline significantly.
So part of the big strategy of raising nutrient levels is to let those other microalgaes compete with dinos, re-establish their population and then eventually outcompete them. But this doesn't happen overnight, especially in a tank in the midst of a dino bloom. It can take many weeks depending on how severe the bloom was.
So there isn't any magical timeline that says when the dinos are gone, in X days the tank will be back to normal. You'll know when the tank is back to normal because you'll see more pods at night, and your nutrient levels will start to balance out and any surviving corals will start to look healthier. It will take some time as the microalgaes will have to start outcompeting the dinos, and then pods will start eating that microalgae, etc. You'll probably have to restock your clean-up crew to be back at the proper level for your algae growth (remember: algae growth is good!). It's a process. But when your tank is healthy and you are past the dino bloom, you'll see it in the health of the tank. Then try adding a few corals and see how they do.
