If I recall, there may be a few steps at initial setup that require a screen, and there are occasionally notifications such as for updates, etc., also requiring a screen. Other than that, you could use it as you describe. You might be able to use an HDMI computer monitor for those instances, if nearby.
There may be an option to have TV without a PVR. Check the lite offerings to confirm.
Edit: The wireless box works without the PVR connected to the network, so if you didn't need recordings, it appears you could manage without it entirely.
I understand that I need a wired PVR to use a wireless cable box. My question is, does that wired box actually require a TV connected to it, or can it sit next to my router, connected to the network as a base unit, but not connected to a television.
The answer is YES. I currently have this arrangement at my house. The Telus installer had it setup this way for me.