No, there is no drafts folder in Messages. Although the message may still be there if you go back to Messages after doing something else, if the iOS needs to reclaim memory from suspended apps, it may not.
If you are in the habit of typing long text messages, I'd suggest you type them in Notes. You can then easily share them back to Messages when you're done. Just tap the icon that looks like a box with an arrow pointing out of it.
As to why there is no drafts folder, no one posting here would be able to answer that. At a guess, though, the assumption is that Messages is for short messages, things one types quickly and sends, unlike email where you spend time composing. You can let Apple know you'd like to see something different here:
Product Feedback - Apple