You would need to select the HDMI input on the soundbar remote to get picture and sound from the stick if you plug it into the soundbar.
ARC is to get sound from the TV to the soundbar. The HDMI input on the soundbar is there so you don't lose one HDMI input on the TV.
No reason not to plug the stick into the TV as suggested above. That way you don't have to change the input on the soundbar.