Had to make an account to answer this one, since I can give unique insight

I'm an atypical case in that I had the Capgras Delusion (along with Reduplicative Paramnesia) in childhood, rather than as an adult. The delusions started sometime around 6-9 years of age. I hid it from others, partly because I halfway knew it was ridiculous, partly because I didn't want to let out that I was on to them...and it caused me quite a bit of anxiety, because I felt like I lost my loved ones and slipped into parallel universes every few days. I would try to keep my eyes on my loved ones, because as soon as I looked away and looked back the feeling that something was different would return.

Sometime around 12-14, I realized how implausible it was for any kind of impostor to conduct such large scale conspiracy, and how implausible it was that I was slipping into parallel universe. I told my parents what I was experiencing and admitted it was irrational. I forced myself to ignore the feeling every time it came (though it still bothered me). Eventually around 17 the feeling stopped bothering me altogether, although little twinges still occured from time to time.

I'm currently in what I would consider to be above average mental health, and many years later learned I the name of the delusions that had plagued me as a child. Prior to identifying them as monothematic delusions, I had thought that imposters and parallel universes might simply be a gifted child's equivalent of monsters under the bed. My parents thought it was from reading/watching too much fiction. I never suspected a neurological disorder until years later.

I'm not sure if I was able to see past the delusion because I'm an atypical case (no known brain injury), because I was a child, because my brain healed via biological mechanism, or because I'm intelligent...but I can tell you that my memory of the event involves me figuring out that the delusion was improbable and consciously working to bring it to an end.

So unless my memories are false (it was a long time ago) or I am engaging in mis-attribution, the answer to your question is that yes, in some cases it would be possible for someone to use rational thinking to overcome this kind of disorder.