It is possible, but it can also be driver related, or the front panel on the chassis could be faulty. What commonly happens is that the USB ports still work, but devices plugged into them may trip the over-current protection, which gives you that "Device has malfunctioned" error that pops up, and puts a triangle next to it on Device Manager.
Two things you can try:
1) Shut down the PC via the command prompt (enter "shutdown -s"), and disconnect the power. Hold in the power button for ten seconds, and then leave it to stand for five minutes for residual power in the PSU to drain. Plug it back in and power it on. Check if the USB ports still display the same error. If they do not, plug in the headset and see if you can trigger the error.
2) Download a Linux ISO (like Ubuntu), and use Rufus to flash it to a USB drive. Unplug unneeded peripherals except the keyboard and mouse, insert the flash drive and reboot the system, choosing the flash drive as your boot device to get into the Live ISO environment. Open the terminal, type in "lsusb" and hit enter. This gives you a list of USB controllers and peripherals registered to the system. Plug in the headphones again, run "lsusb" again and see if the headphones/mic pop up as expected. Test them while a video is playing and see if you can trigger an error where they don't show up after running lsusb by testing all the available ports.
The reason why you'd use Linux is to isolate if it is a driver issue or something hardware related, as the Linux kernel won't be using the same drivers Windows does. Linux kernel drivers implement USB power delivery in a standardised way, while the vendor drivers may have funky methods of getting things working.
If the error goes away after draining the PC of standby power, then you have something to work with. Check your wiring, check your ports for any rusting or damaged pins or fingers inside the ports, and try isolate which USB port displays the issue. As in, figure out if it's the front-panel I/O or the rear I/O ports.
If it's front I/O, you might have a faulty front panel. If it's rear I/O, you could be looking at anything from a BIOS bug to a motherboard issue, or a slightly noisy 5V rail from the power supply.