In the near future, the human population is overcrowded and food and water becomes scarce. Every preventative measure failed to address this issue and the world falls into a turmoil and panic is everywhere. It was suggested that humanity is one of the creatures that have sex for pleasure and decided that we should nerf the brain reward system. Then many governments gave in to corruption and pressure from a series of nationwide protests. They launched a campaign to force everyone to take a pill (nanites) that can kill pleasure while having intercourse. Such extreme measures are becoming popular with many big companies due to the increasing demands. Ok I think you get the idea but I suspect being a human goes beyond biology but I cannot think of what grave consequences if the plan goes well.

No.

The drive to have a child is one of the strongest ones out there. Not everyone wants a child of course, but a great many people do. We humans may get children via intercourse but that is not why we want to have them.

Lots of couples right now have sex for procreation even though they're not getting much out of it. Some people have sex with people they're not really into or in a relationship for the purpose of getting pregnant. Other couples and singles use artificial insemination to have kids. It's easy to do this at home and many do.

Also, sexual pleasure is not the only thing people get out of sex. Emotional intimacy is a huge one and a lot of couples who are meh about the sexual pleasure still want to have sex. There are many other reasons people have sex as well.

This question makes a lot of assumptions that have no basis in fact. Call it a frame challenge. Your beliefs about "reward" don't hold water.

If your scenario came to pass, people would likely have less sex than they do now. Some people would have less in general and a larger percentage of people than now would have none.

As a general rule, this would lead to fewer pregnancies, though it's not as straightforward as you might think. It also means more (but not all) pregnancies would be planned, so fewer abortions and adoptions. But don't assume it's linear. If a couple (who doesn't use birth control and doesn't plan out cycle timing) goes from, say, having sex 20 times a month to 10, they aren't going to have half the number of pregnancies. It probably won't change much, if at all.

Note that I'm not addressing changes in contraception use. A society with the population pressures you mention will be high users of birth control. Much higher than we have now, and we use birth control an awful lot in most countries. Couples who have sex for reasons other than sexual pleasure may use birth control more (since any side effects of lessening pleasure don't matter) or they may use it less (under a mistaken belief that pregnancy rates are correlated with amount of sex).

The rise in population would slow and maybe even reverse. Eventually, the population will stabilize because people will choose to have children based on things that have nothing to do with how often they have sex.

The simple answer is no. The human species will not go extinct.

If governments can legislate and enforce the world's populations into taking a pill to abolish sexual pleasure, it will be an even simpler step for those governments to regulate reproduction. This have additional benefits. It will make economic planning and resource management so much easier. It will alleviate and ameliorate demographic pressures on forward social, political and economic development.

In an overpopulated world, well regulated reproduction will make the process of reducing the global population to long-term sustainable levels a much easier task.

Families also want to reproduce and have children to carry on the family name, inherit assets and property, have someone to look after you in your old age, and so on. Sexual pleasure is not the sole driver of reproduction.

Large-scale family planning can be managed to allow people to manage their careers and have families of their own without disrupting those careers.

Sex by itself is not the only means to ensure reproduction. Artificial insemination and in vitro fertilization technologies have been improving. Assuming this will improve in future, conception will become as easy as a visit to your GP.

Many of the world's religions will embrace the change. The majority of people won't be running off to indulge themselves in illicit sexual liaisons. Sex before marriage, adultery, pornography and prostitution will be a thing of the past. People will only think pure thoughts. Productivity will rise.

A sexual pleasure free world will be embraced as a better, purer world. Even in the absence of sex, the species will continue to reproduce the social, familial, economic, political and demographic pressures are too great to allow extinction to happen. It will make the reduction of excess numbers of people easier to manage and it will alleviate the problems of an overpopulated planet.