Yes. You can breastfeed and pump at the same time.
The pump's tubing can be tucked away or if you're using a Philips Avent Hands-free Electric Breast pump, you can clip it to the tube coupler, which helps limit noise from the motor unit.
You can also disconnect a tube from one of the collection cups and move it out of the way (the motor unit will still work correctly).
The cap can also be rotated between four different positions for comfortable pumping and breastfeeding.