Can I use Alfa long distance Wi-Fi with AppleTV AirPlay?
The Alfa WiFi signal booster will work with many WiFi radios, if it is the right model and has the right driver for your OS.

If you are going to need the WiFi signal booster Antenna (Alfa long distance) will depend on your location.

Your Alfa antenna has to come with OS X drivers like this model:

http://www.crucialwifi.co.uk/Alfa_Network_AWUS036NHR_V2_bgn_LongRange_USB_Adapter_rtl8188ru/p740998_3940899.aspx

Normally a "well placed" wifi extender/repeater would be enough to bring your wifi signal to the floor below you. I have Netgear N300 for my wifi network around the home. Just plug it in wall socket in the stairwell somewhere. You need to know that the wifi speed will be cut in half, but still will be enough for Videos streaming from youtube etc.. if your original is strong.