George, it shouldn’t be horrible. Note the wifi 2.4GHz & zigbee interference chance. They operate in the same frequency band;
Explanations and hints here: (note, you don’t have to install anything)
When you want to measure the pollution of (neighbour’s) wifi channels in your home, you can use wifi analyzer (android) or Network Analyzer Pro (iphone)
Also adding one or two mains powered zigbee devices can make thing less horrible. They act like a router/hop/extender
