If there is no open source driver for the Wi-Fi Module you won’t be able to install it on pure PureOS and need to make some kind of Frankenstein OS out of it by including Debian repos and install it from there not sure that works in a live environment.
You can find some info about it in this thread https://forums.puri.sm/t/terrible-wifi-performance-with-librem13-librem15/
Also you’d probably have the exact same problem with the Wi-Fi Adapter on the Surface.