Yes, translation can be sent to an outside company. For example, court rulings are obviously not translated by the Translation Bureau. In New Brunswick, all of those decisions are translated in the private sector by the Centre de traduction et de terminologie juridiques, which is part of the faculty of law at the University of Moncton.
At some point, the government began privatizing certain services, which raised a lot of concern within New Brunswick's francophone community. The government would also like to privatize the translation of some court decisions. However, there are concerns about quality. Perhaps regular texts could be translated in the private sector, but legal documents are likely a bit more complicated.
Right now, attempts are being made and there is a desire to use private sector translation companies. However, New Brunswick's francophone community is very concerned about the quality of the texts.