I have an adult child who has a medically diagnosed condition but has not applied for a disability. My wife and i support her totally. Can I claim her as a dependent?

You can claim her as a dependent. You can claim the Canada Caregiver amount for her and say she has an infirmity if you have a doctor's note saying so. 

I would recommend applying for the Disability tax credit. Print out this form for her doctor to fill in.  

http://www.cra-arc.gc.ca/E/pbg/tf/t2201//