In some cases, absolutely. There may be lower incidence of isolated depression or anxiety, but a lot of mental illnesses are hereditary rather than strictly environmental.

I'm autistic, and i had no idea until i was 26. When i was a kid, my executive dysfunction wasn't a problem because i had my family to rely on. I never had to worry about money because of scholarships and grants for school, so my dysfunction only came out as procrastination in school. Now that I'm an adult and trying to take care of myself, it's coming out in the inability to keep my apartment in shape or feed myself. All of my energy goes into my job and there's very little left over for basic life tasks. If i had money, i may still not know because i wouldn't have to worry about cooking or cleaning or anything beyond work as it is. I could pay someone to make phone calls and appointments for me. Most of my dysfunction wouldn't be apparent if i had someone else helping me.

So i definitely think certain symptoms or disorders can go unnoticed in wealthy people even though they do still experience the disorder itself.