Can hair loss effect a person's psychological state?

Yes it's definitely true when I dye my hair brown instead of old and gray I feel a lot better when I look in the mirror and I see myself old and gray it's depressing.

When I put the artificial hair in the bald spots. It makes me feel better when I see myself with bald spots and gray areas and I make it look young again it makes me feel better.  

Even though I know it's a lie I still feel better looking younger in the mirror

Yes of course.

You will get depression first.

Yes.  Usually it engenders feelings of being unattractive and obsolescence.