You can do that ,but need to access their phone once, because you need to scan the QR code from their phone’s whatsapp to access whatsapp web.
Once the QR code is scanned, you can open the browser at later point of time and can access the whatsapp messages.
However, if other person disconnects the whatsapp web, then you may again need the phone for scanning whatsapp web QR code.
I hope this will help.
