Can the travel consulting company sign up for the tour on behalf of the guests?

Of course. Entrusted tour group means that the travel agency entrusts other travel companies to organize tour groups, which is usually called individual package tour. The contract says which travel company to entrust, which requires the consent of the guests. The entrusting group needs to find a qualified company. If it is a self-organized group, it is the travel company that signed up for the group to travel with it.