Yep if the aircraft has 2 radios, during my IR I was taught to monitor the ATIS on the second comm set but with the volume low so you can just about hear it but it wont interfere with ATC communications.
As for not listening to the departure ATIS the instructor must must be mad!! When you are commencing an approach, especially if into an unfamiliar airport, you want all the info you can get. Ask the instructor how he would know if any rwys are u/s if he didn't get the ATIS? Apart from asking ATC loads of questions and generally blokcing the airways you can't! The ATIS is a valuable source of info and to ignore it when its provided seems mad.