No, that's not totally correct.
Sam & Cat is not a sequel to Victorious nor to iCarly, it is a spin-off that needs to be seen as a stand alone show which occassionly throws around references to the other two shows in order to attracts those fans.
The members are indeed still going to Hollywood Arts, but it's not known if they all still attend Hollywood Arts. Only Beck, Jade, Cat, Tori, André and Robbie are confirmed to attend the school as seen in #MommaGoomer. Trina, for example, could be graduated for all I know. Sikowitz is the only one of the staff to be confirmed as a staff member in Sam & Cat, all the others can possibly still work there, but could have found another job as well.
Cat is not the only character we still see, we also saw Jade, Robbie and Sikowitz in a guest appaerance and the backs of Jade, Robbie and the others in #MommaGoomer.