Home Sharing and External Hard Drives
Can your movie library be on an external hard drive while iTunes is running on a computer with home sharing turned on so it will stream to Apple TVs in your home?
Question marked as
Sure, that is possible. The Computers app on the Apple TV box will seek sharable libraries on the home network, as offered by computers with the iTunes application (PC or older Mac) or with the Apple TV app (newer Mac). It is then up to the computer to access the wanted media file; it can be on an internal disk, external disk, or even network attached storage, as long as it is accessible to the computer, and linked in the library. You will have to change the application settings for the location of library items, or not aggregate at all and link everything manually.
Use Home Sharing to share media from a computer to other devices - Apple Support