Great question that can also be useful to other forum users. One must distinguish hardware effects from software effects. Hardware effects are machines on which the sound wave is modified, filtered, inverted, etc., physically, meaning where appropriately designed electronic components provide the modification of the sound wave. Software effects are programs that, by analyzing the sound wave, filter it and produce a new filtered one. In hardware effects, all this happens at "run time"; in software effects, this does not happen. There is indeed a period called latency, during which the software analyzes the incoming wave and returns the filtered wave. Latency depends on the performance of the machine being used. The human ear cannot distinguish the difference between two signals transmitted with up to 20 milliseconds of latency. From 20 milliseconds onwards, one begins to notice the phase shift. In other words, when you connect a microphone to the computer and start recording, in the presence of many effects, if the latency exceeds 20 milliseconds, you notice that what you hear in your headphones is delayed compared to when you actually pronounced those words into the microphone, and this can be annoying. If the latency is excessively high, it becomes impossible to sing because there is too much phase shift between live singing and the "what you hear" in the headphones; this phenomenon causes you to go out of time. To summarize, you can use real-time effects during recording if these effects are hardware, i.e., machines connected between the microphone and the audio interface. I recommend post-processing anyway, also because you have more ways to make changes and you are not subject to having your ear spoiled by a sound that is not the true sound you emitted. However, there are people who are so used to singing with reverb that they would not be able to sing without it; in that case, they are forced to use effects. My opinion, however, is that dry and pure sound, whether produced by an acoustic instrument or by the voice, should always be recorded as it is, without effects; this way we are more focused on exerting maximum concentration to ensure there are no errors. A drier sound is indeed harder to manage, but it is also true that it makes you realize better where there are imperfections. Filtered, colored sound, or sound to which reverb has been added at worst, can camouflage mistakes if listened to again in the original version without effects; however, the opposite never happens! Once you have recorded without effects, there is always time to add effects to enrich the sound.
Not by chance, speaking some time ago at the conservatory with Maurizio Colonna—who, in addition to being one of the greatest classical guitarists in the world, also owns a recording studio—we found ourselves in great agreement on this topic. We were discussing how to record a piano... Positioning AB microphones near the hammers to also capture the mechanical noise that makes the true sound of the piano, without effects and, only subsequently, at the end of the recording: post-production.
In addition to all this, dedicated hardware effects are often used in live settings rather than during the recording phase...
Best regards