If I add a power amp to my NAD receiver....

If I were to add a power amp to my NAD receiver would the speakers be driven by the receiver, power amp or a combination of the two?

And, can a power amp be added?
If the receiver has preamp-amp jumpers you can connect a power up. The receiver amplifier would be bypassed. If you don't have preamp out on the receiver there is no easy way to use an external amplifier.
Most NAD receivers I've seen have a "pre-out", so you should be able to add an external power amp. Doing so will bypass the internal amp, the external amp will be your power source. Make sure the external amp is at least twice as powerful or you won't hear any volume difference.

Before adding a power amp, I would replace the ugly pins that come standard with NAD bridging the preamp out/power in with good quality jumpers. This will improve the unit substantially and you may find no need for a new power amp.
Assuming your NAD receiver has preamp outs, which it probably does, it's possible to power your speakers from only the new amp or from both the new amp and the amp internal to the receiver. This second option is called biamping and the manual for your receiver may discuss this in detail. If you feel that your receiver does not have enough power for your speakers and your speakers have two sets of binding posts, then biamping would be something to consider.
Depending on your model, you can do "both." You can add an extermal power amp while still using the internal amp for a bi-amping configuration, assuming you have bi-wire loudspeakers.

This was a nice feature of the C series receivers and power amps. These receivers had a "matching" power amp so you could combine them and know that gain would be the same for both. The pre-outs of the receiver could feed the power amps.

In fact, I think these receivers even had an adjustable gain control so you could level match a different power amp (instead of using NAD's matched set).