From my test, ADH will not log when the conversion fails. However, the consumer application receives the blank value for that field. It seems that ADH sets the value to blank when the conversion fails.
Issue with logging item-level, and even worse, per-message events, is that depending on the rate, it will fill up and overflow your log file (blowing away important component-level log information along the way), and also may impact the performance of the component. For inserts/posts, TREP has an option to NAK on conversion failures, but as mentioned, only indication on southbound conversion is blank data. An enhancement to consider would be to add a shared memory counter for the number of times conversion has failed along with an option to log once every for example 100 events (many times it's the same event over and over).