TL;DR: Women rates funny guys as more intelligent. Are professors the same?

No, not really. In ordinary conversation, nobody is expected to say anything deep or knowledgeable. Making a joke at least shows more cleverness than many of the alternatives (such as chatting about the weather). On the other hand, in a context where you might be expected to say something with real academic content, just making a joke instead suggests that you don't have anything else to contribute. I think it would be better to try to engage with the subject matter, even if you are clearly not an expert yet, than to look like you are deflecting the issue with a joke.

The worst case scenario is making a terrible joke and seeming overly proud of yourself for making it. Don't write to someone doing gene editing and say "Your recent papers are really impressive and have been getting crisper and crisper (get it? LOL!). I guess mi Cas es su Cas, am I right?"

Well, if the joke is taken as funny, that could be a very effective way to develop a rapport with a potential PhD advisor, stand out from other applicants, and assess whether it is the sort of advisor with whom you would enjoy spending the next three-plus years. But it is a risky strategy if your sense of humour does not align with the advisor's right at the outset of contact.

More importantly, I have the suspicion that you might not be identifying the most effective types of questions. While asking questions about the advisor's research at least shows that you are familiar with it and have taken the time to investigate his group, specifically, you will get more mileage by showing that you can think of new research questions that expand on the work his/her group has already been doing. Is there a direction unexplored in his/her recent research that you find quite fascinating?

Though the the psychological aspect might be true, it wouldn't be advisable to use it under this context. Even if it is amusing, your research proposal itself might be mistaken to be just a joke.

Your sense of humour should be something to be witnessed in person. Bear in mind that sense of humour is only a supportive quality; it is your primary skills set and research passion is what would make the initial impact.

J'aborderais cette question en me basant sur une question de risque / gain.

Le risque de la blague est que vous soyez rebutant, offensant ou que vous causiez des dommages à votre application. et y compris la perdre.

La récompense est que la blague inspire une sorte de sentiment «J'aime la coupure de ton foc» chez le professeur, et augmente légèrement vos chances de succès.

Vous y réfléchissez trop.

Vous n'êtes pas tout à fait sûr d'inclure la blague, mais l'omettre ne vous fait pas du tout de mal. Alors laissez-le de côté. Vous perdez votre temps à transformer cette trivialité en une question détaillée et à attendre des réponses.

Short emails are better

Don't out everything into one big email. It will only end up in the todo pile, or be scanned for "what does this guy want from me?"

Consider asking to-the-point questions on his research.

Fact is that research has shown you are more likely to get an answer if your email is really short.

So use this strategy to start a discussion. Chances are that he'll invite you to come to his office (use a university email, so he knows this is an option!)

Once you've sent a few messages back and forth, you'll be able to tell wheter or not to make that joke. Your chances of getting an offer are also much higher if he perceives you as "persistent and curious" about his research.