Can someone overcome repeat drug addiction without going to rehab?

Sometimes. Overcoming addiction is a process and not a place. You have to certainly detox off of your addicting substances, of course. But you really need to change the people that you hang out with and frequenting the places that your get your drugs. It is possible to do. Many patients benefit from suboxone for opioid withdrawal avoidance. It can be done diy but it realies a lot more on your determination.
Yes. Many people do recover from addiction without rehab. Many people recover by attending 12 step meetings such as aa. Some people recover without even meetings. What recovery takes most is a strong willingness for change in ones life and using the necessary "healthy" means of achieving it. Wishing the problem or wanting the problem to go away does not work. Being around other healthy people is a must.