Having "cd foo" potentially take you to an entirely different location can be dangerous, to say the least.
rm -f *
And you do know that CDPATH also affects shell scripts, right?
I hear what you're saying, though I'm not really persuaded by this argument. When you 'cd' into a directory along your CDPATH, Bash will print out where you end up when you arrive. Here's an example of what I mean (easier to see than explain):
circe ~ ❯❯ cd bin
circe bin ❯❯ cd ithaca
circe ithaca [master•] ❯❯
> And you do know that CDPATH also affects shell scripts, right?
No, I'm embarrassed to say, I never thought of this. And this part does sound like a potential problem. When I write Bash scripts, I always use full paths, but I see where my having CDPATH set puts me at danger from other people's scripts. Technomancy gives a concrete example above. Although I think this is bad practice on their part (not to use full paths), I appreciate the warning.
However, your question suggests that you're probably one of the chosen few who could actually use this feature safely. My general advice against it was aimed at the 99% other people who think "Oh convenient!" without being fully aware of the implications.
So, no, Bash doesn't implicitly export the variable. (Thanks to everyone for helping me improve my dotfiles a little bit.)