Is it possible to detect a mental disorder from online writing?

You could if they start writing stuff that is confusing. It really depends.

Some people have depression or anxiety or P.T.S.D. but they know what is happening and how to behave but the above is considered mental health.

Eh j would guess it's possible for most mental disorders but people with personality disorders are impossible to detect based on writing style or even topics

For some reason, people always tell me I write novels whenever I email people. I just feel i need to be very detailed in my answers. for some reason i was diagnosed with paranoid schizophrenia.

its possible to highly suspect,  once I could tell a girl was manic (bipolar) by her writing.  Another time I picked up on signs of autism.

It depends on how much they "write".

By writing on different topics, someone who is a trained and licensed mental health professional can get at least a working diagnosis based on what personality traits they present and what symptoms they talk about. 

But don't forget, there are a lot of attention-seeking trolls out there.

it depends on the person

So many different mental disorders.

You cannot generalise about all of them.

Some may show some indications of some disorders in writing style. Others can simply be mimicking then.