Can the Kraken V3 Pro be used in both wired and wireless simultaneously?

I’m in the market for a new headset and one of the most important thing for me is that if I can use the headset wired and wireless at the same time. I can’t seem to find a direct answer to this though but I have found that some headphones won’t turn on if they are using the AUX feature or the Aux feature will not work if the headphones are connected wirelessly to a device but no one seems to market this and it makes it hard for me to find out if this can be done. I want it to work so I can hear my PC audio (discord, videos, ect.) wirelessly and have the AUX cable connected to my Switch.