Generally, no a person can not be convicted of a crime without having knowledge of the conviction. However, there are only two ways this can happen if at all. First; when a person is charged with a crime he/she is expected to appear at each court appearance but if they are read warning that a trial can occur in their absence should they fail to return to court it is possible there can be a trial held if the defendant fails to appear for the trial leading to a conviction. However, the person would have known there was a trial and just chose to not appear in court.
Second, if someone is arrested or issued a ticket using a fake name and information that is NOT based upon a fingerprint search resulting in the wrong person being convicted. This last example is an extension of identity theft, as it is rare but possible in some of the small town that don't run fingerprint checks on everyone immediately.
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