It's weird but no, and here's why.
In the Matrix, you are represented as a icon called a persona. A persona is basically a user entity such as my profile page, except that in Shadowrun my profile probably has mechanical wings and a gatling gun. This icon technically shows up as long as I'm connected to the Matrix and not running silent. All of this assumes I'm not a technomancer. Which means as long as my commlink is on and connected to the Matrix (any grid), it's there. If people look at me in AR they probably see an overlay of wings but not the gatling gun because that's the icon of my attack program and I don't walk around with a hacking program loaded. I don't need to be concsious for my persona to show up. If people are in VR and they look at my icon, they'll see the full aspect of my persona.
Now I'm on the run and I sit down and connect to the network in VR my body is left behind. Note that it says my physical senses are overridden by my Matrix senses (I can't feel anything from the outside like temperature, attacks, need to pee etc.). I'm in full control of my persona. If someone finds my body and decides to taze me until I'm unconscious, my mind is not longer in control of my persona, but my persona is still logged in.
Technically, when you are doing something in the Matrix, your brain is giving commands to your persona, a software running on your commlink, which then compute the action you want inside the system. If you are unconscious, you can't take actions/don't give commands to your persona, but your persona is still subscribed (aka connected) to the node. What can sever that connection?
There are 2 ways to be disconnected from the Matrix. Physically (pulling the DNI nodes, breaking the commlink, server shutsdown for some explosive reason) or digitally (Jack out action, logoff action, taking too much matrix damage and dumpshock etc.)
Technomancers are the exception because they project a living persona which requires to be conscious (p.239 Core 20th anniversary edition).
The weird part is that I had to read a lot in the core and put pieces together to get this answer and there's no clear indication of it. There's no single paragraph that tells you that. I think they fixed that in 5th edition. I would have to check.