Just tested it and didn't lose namtar's ward or other items. I always supposed the insurance is only for the items you aquire on the way, which is why i never used it.
So this post is a bug report for either you or me. Or you have been attentive so far and never died with an important item from the locker.
Although you're not fully testing it if you don't convert it once you reach level 10
That is true indeed. Then again i would convert it in a "serious" game only, if it ensures a victory.