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If I understand your questions correct, as in connected to both but not playing the audio from both at the same time?! Then yes, it's possible. I run the same setup. PS4 and PC on my desk and Arctis connected to both so I don't have to change wires or settings when switching where I need sound from.
You'll need to buy a bit of extra bits though. Let me elaborate:

• 1: To get the best sound you want Toslink connections to both and USB to both for power and chat-mix. You'll need both a toslink and USB splitter. NOT a Hub. Something like this: https://www.amazon.de/CSL-%C3%9Cbertragung-verlustfreie-Signal%C3%BCbertragung-Hifi-System/dp/B0130TX40U
  You need 2 IN and 1 OUT (!!!). You'll then connect both the PS4 and the PC to the 2 IN ports and the OUT port goes into the transmitter.
  
  You'll need to do the same for the USB, get a similar box:
  https://www.amazon.de/dp/B01CU4QCRS/ref=psdc_430058031_t2_B074TYDJK2
  Connect a USB lead from both the PS4 and the PC to the IN ports and the OUT port goes into the Transmitter.
  
  My two splitter boxes have hardware switches so even if both devices are running, I can toggle sound with a button push (USB switches automatically but toslink is manual). I find that better than auto switching, especially when both are running.
  
  
• 2: If you have it set up like this you'll only need to configure one input on the transmitter. For me that's the PS4 mode so it defaults to Toslink in and Party Chat from USB. All the settings in the box are made for that one connection so whichever feed I'm running into the transmitter from the switch above, gets the equalizer/chatmix settings.
  
  
• 3 Bluetooth is separate so my solution works the same as bluetooth and PS4.
  
  Again, parts you need:
  
  
• 3 Toslink cables (2 from PS4/PC into splitter, 1 from there to Transmitter)
  
• 3 USB cables (2 from PS4/PC into splitter, 1 from there to Transmitter)
  
• Toslink splitter/switcher (2 IN and 1 OUT at minimum)
  
• USB splitter/switch (2 IN and 1 OUT at minimum)
  
  If your PC supplies USB power while it is switched off, the Transmitter keeps getting power to recharge the batteries. Make sure to set the Display to timeout in that case to avoid burn in!
  
  So with a bit of extra hardware it is possible and works a treat. You can get real short cables to keep it tidy. I mounted the switches on the wall and have just enough length to get to the boxes.