Is it possible to airdrop a video/photo to another ios device while playing it using airplay?
It depends on the app and how many copies of the document in question you have on the device. I can't think of an app that does both at the same time, but the plumbing is there as long as the app doing the AirDrop doesn't try to play the media before you send it.



I can easily enable airplay and use the music player app to play music. While the music is playing, I can airdrop pictures from the Photos app with both happening simultaneously. So nothing on iOS prevents both from being active in general.

In fact, I can run any other app I want while AirPlay is going on with one catch. Only one source of media can play at one time. Specifically, things that the control center can play or pause or change volume is "media"

If the foreground app attempts to play sounds or video, that playing will automatically pause the music app from playing in the background but not affect the AirPlay settings. Since iOS handles muting the background sounds or video when another app requests play permission in the foreground it will pause the any multitask operation that was previously playing media.