Based on another question here, I think it is legal, but I would like it directly from the people who know. Thank you for your time.
Yep, according to FCC part 97.115...as long as the licenced control operator is present and supervising. There is at least one exception though - the third-party operator cannot have previously had a license revoked.
Here is section 115:
§ 97.115 Third party communications.
(a) An amateur station may transmit messages for a third party to:
(1) Any station within the jurisdiction of the United States.
(2) Any station within the jurisdiction of any foreign government when transmitting emergency or disaster relief communications and any station within the jurisdiction of any foreign government whose administration has made arrangements with the United States to allow amateur stations to be used for transmitting international communications on behalf of third parties.
No station shall transmit messages for a third party to any station within the jurisdiction of any foreign government whose administration has not made such an arrangement. This prohibition does not apply to a message for any third party who is eligible to be a control operator of the station.
(b) The third party may participate in stating the message where:
(1) The control operator is present at the control point and is continuously monitoring and supervising the third party’s participation; and
(2) The third party is not a prior amateur service licensee whose license was revoked or not renewed after hearing and re-licensing has not taken place; suspended for less than the balance of the license term and the suspension is still in effect; suspended for the balance of the license term and re-licensing has not taken place; or surrendered for cancellation following notice of revocation, suspension or monetary forfeiture proceedings. The third party may not be the subject of a cease and desist order which relates to amateur service operation and which is still in effect.
(c) No station may transmit third party communications while being automatically controlled except a station transmitting a RTTY or data emission.
(d) At the end of an exchange of international third party communications, the station must also transmit in the station identification procedure the call sign of the station with which a third party message was exchanged.