That make no difference to Channels.
Stay signed in, or "Remember Me" is just a thing local to that web browser you are using to log into your account. It stores a Cookie in your browser cache so that u will not have to re-login again if you close out the browser.
If you use a different browser on the same computer, you will have to login, cause that browser does not have the Cookie.
Channels sever is its own "web browser" thing when it loads the Xfinity TVE login page in the background and there is no way for the user to see or modify that page, it just shows a screen shot of it when it fails.