You should be able to plug in multiple gamepads and have it work. We do that through a SteamLink. Unfortunately, I know not every gamepad is detected out-of-the-box by Unreal Engine, so I'm afraid if your particular hardware won't work... it just won't work.
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For what it's worth, from within Steam, you can go to Games menu, then Add a Non-Steam Game to my Library. Put in the path to the executable, and presto, it shows up in Steam and can be called via Big Picture mode. This is how my kids and I have been able to play a few of the Epic Games Store giveaways from the family room TV.