No. The YouTube integration lists your channel's videos, reads their analytics (such as views and watch time), and picks existing videos for Google Ads video campaigns. It doesn't upload videos.
Connecting: YouTube uses your own Google Cloud OAuth client with the YouTube Data API v3 and YouTube Analytics API enabled; one-click isn't available. Add the redirect URL from the field help.
Choosing the channel: after you connect, pick the channel. With a Brand Account, you choose it in a window.
An empty channel list means the Google account you signed in with has no YouTube channel.
More: connecting integrations and YouTube integration.