Can my unlicensed assistant ask consumers who contact my office whether they are represented by another broker?

Yes, but keep in mind that according to TREC rules, your unlicensed assistant may perform administrative tasks that are clerical or secretarial in nature but may not solicit business. If you choose to task your unlicensed assistant with gathering personal information from consumers who contact you, make sure their questions do not veer into soliciting or negotiating for services where a license is required.