I don’t think that it is a good idea. It drastically increases the complexity of logging, and the log is intended for the developer / technical support anyway. Those people should be able to understand English logging.
In fact, for my projects I insist on the whole source code being in English, including comments and variable names. What is the most important factor here IMHO is that localized logging and/or ‘localized source code’ is always inconsistent as there will always be nonlocalized parts (e.g. in APIs, librariers, etc.).
If you are used to English logging messages for, say, an SQL framework, then getting the very same messages in German can be very confusing - even (especially?) for a German. With German messages (for example, the Java XML parsing produces those) it takes quite some time to figure out what is actually meant.
And even worse: Try to search the web for a localized logging message. The probability of anyone having solved your particular problem in YOUR language is next to nil - except if your language is English.
I think internationalization should be limited to the GUI / user-exposed features of an application.