Yes, you can use your Arctis Pro Wireless or Arctis Pro + GameDAC with a PS4 Slim, but will need some way of connecting to optical audio in order to use all of the product’s features such as surround sound and ChatMix.
There are generally two ways to do this. First, check if your TV has an optical audio output. If it does, you can connect an HDMI cable from the PS4 to the TV, then connect the optical output of the TV to the Wireless transmitter or GameDAC. You will also connect the USB cable to the PS4.
If your TV does not have an optical audio output you can use an HDMI Audio Extractor, (such as this one: https://www.jtechdigital.com/j-tech-digital-premium-quality-hdmi-to-hdmi-audio-spdif-rca-stereo-audio-extractor-converter.html). With this device you will connect HDMI from your PS4 to the audio extractor, then connect an HDMI from the extractor to your TV for video. Next, connect an optical cable from the extractor to the Arctis Pro Wireless base station or GameDAC.
You can forego using optical audio and simply connect USB to the PS4, but you will not be able to use surround sound or ChatMix features. If using this setup you will also need to set the Wireless transmitter or GameDAC to their PC modes. This setup will provide basic audio, but is not the recommended solution.