It's not a good idea. Also, that trick is older and more popular than you might think.
As with any security-through-obscurity pattern, it only works if the adversaries aren't aware of it. But since saving emails as drafts instead of sending them has been popular among criminals, terrorists and even found its way into pop culture, that technique rather attracts attention and certainly doesn't add security.
E.g., one popular case was the Petraeus and Broadwell affair:
The CIA director and his biographer had a shared Gmail account and wrote some of their personal missives as draft emails, which were left in a draft folder or an electronic, "dropbox".
[...]
Al Qaeda terrorists began using the technique years ago. It allowed them to exchange information without sending traceable emails. An account would be opened by one conspirator and a draft email written and saved. The account could then be opened by a co-conspirator with access anywhere in the world, who could read the draft email and delete it.
The process meant the information had never been sent in the form of an email, making the electronic trail weaker. The technique has since been copied by teenagers in many countries to avoid having their emails monitored by their parents.
(Source)
If you change a draft or delete it does the server preserve the drafts if they are never sent?
There is no way of knowing if deleted drafts are preserved, so better assume they are kept. Also, getting behind this trick might be as easy as searching the provider's database for email accounts that produce high amounts of drafts but rarely actually send emails.
Instead, encrypt your emails. There are plenty of cryptographically secure technologies, free providers and VPN services to do so anonymously and securely.