Is it possible to book my flights via the Emirates website, then call Emirates holiday to book the hotel so both are combined?
Yes, I have done this. However, it depends on the sales person. Make sure to check with your local office before going ahead.
As mentioned above EK holidays have their own fare bucket which at times is cheaper than the online price. However it only acccrues saver miles. Depending on what is your priority you can select which route you wish to pursue.