No, I don't believe that the fear of getting AIDS is really stopping anyone from having arbitrary sex anyway. It's super easy to get not AIDS: just wear a condom! Even if the condom breaks, the chances of getting AIDS is extremely low; the virus-infected sperm would have to make its way to the blood of the recipient in some manner. This means that you would have to get a small cut in your skin that is interacting with the sperm.
The only common way to get AIDS is by having unprotected anal sex with someone that is infected by AIDS/HIV. So just wear a condom, and maybe don't sleep with people who have AIDS, and you will be fine.
So I don't think a treatment for AIDS will chance anyone's behavior towards arbitrary sex.
As a side not, why would more arbitrary sex be bad? Why should we care about how many people other people have sex with?
Herein lies one of the cultural difference between the more progressive West and the conservative East.
There are still cultures that exist where sex is regarded as something dirty taboo. And as a person who comes from such a culture, I can say that technology is not the main driver of cultural change because a person might have the latest smartphone and the fastest internet connection, that does not directly make said person more progressive and open minded...
There's a saying here in my country in English, "The Internet aims to bring the world to the Kampung (village), but instead the internet brought the Kampung to the world".
Yep, there's definitely a huge culture clash between the East and the West on certain parts of the Internet. We have a lot of different views on some "taboo" matters, especially things like sex, homosexuality etc.
That's a great saying!