I ain't the man™, but I'll answer anyway.
The answer is "no", but there are things you can do.
You can write an agent to delete all docs older than a day, for example.
If you're just using OpenLog in a single app, you can edit the script libraries, stick a constant like
Const OPENLOG_DISABLED = True
and then put
If OPENLOG_DISABLED Then Exit Sub
at the top of the functions you use. By using the constant it's easy to enable logging by changing it to False.
Or if you can't make changes to production code easily, you could use a profile document rather than a constant.
As another developer, I'd urge you to reconsider whether or not you really want to turn off OpenLog. Provided you automatically delete old log documents, it's a really good tool for being able to check up on applications and be automatically notified when something goes wrong.