Legal Question in Criminal Law in Texas

Without more information, it's difficult to say. Just because he received deferred adjudication doesn't mean that the arrest/deferred won't appear on his public record. He has to file a Petition for Non-Disclosure to get the matter sealed from the public. If he hasn't done that, than a background check will likely reveal the case. An apartment complex can reject someone who has a criminal record.

If he wants to seal this matter, he should speak to a local criminal defense attorney.