I don't think this is a good tactic when you have an audience that is even halfway awake. when I see this happen on a topic I'm not very familiar with, my first reaction is to think it was an incisive question that OP realized they did not have a good response to.
I find that there is usually a fairly small number of "gotcha" questions that come up over and over for a particular topic. the "trans people in competitive sports" question in this thread is a good example. what makes these types of questions rhetorically effective is that they're usually at least half-rooted in truth. in my experience it's more effective to recognize the likely gotchas and have a response ready, or better yet, preempt it entirely. at the very least, you should explain why you're not answering the question, lest it appear that you are the one arguing in bad faith. you have to keep in mind that you're not just trying to convince your interlocutor but also your audience.
I find that there is usually a fairly small number of "gotcha" questions that come up over and over for a particular topic. the "trans people in competitive sports" question in this thread is a good example. what makes these types of questions rhetorically effective is that they're usually at least half-rooted in truth. in my experience it's more effective to recognize the likely gotchas and have a response ready, or better yet, preempt it entirely. at the very least, you should explain why you're not answering the question, lest it appear that you are the one arguing in bad faith. you have to keep in mind that you're not just trying to convince your interlocutor but also your audience.