All Airline Cadets at FTA require to have a valid Student Visa if they do not have Citizenship, Permanent Residency or another suitable visa. The information on the Private Aviation Training link is equally applicable to private individuals as it is sponsored airline cadets.
Under the DIAC rules Student Visa holders (aviation related or not) can apply for the right to work for up to 20 hours per week..and this is usually granted. Indeed many students outside aviation do work to help fund their drinking money at weekends!!!