It is possible in Lightroom, but not directly. The same method should also work for Capture One.
I use qDslrDashboard to automatically download all pictures taken with the camera. Then Lightroom is configured to monitor and auto-import images from the download folder. I can control the camera via the computer, or shoot with the camera directly, and have images automatically show up in Lightroom. Capture One should also have the ability to monitor and auto-import from a folder.
qDslrDashboard works only for cameras with WLAN, which includes most Nikon, Canon and Sony cameras. It is free for Windows, Linux, and Mac. For iOS and Android, it costs 10€, but has more functionality than the Nikon app.