Is GTA Online in GTA 6 on day one?
No.
Viral claim: “There's no GTA Online on day one” True
No. GTA 6's PlayStation Store page says it in one line: "Grand Theft Auto VI is a single-player experience." The listing says one player, and neither Rockstar nor Take-Two has put a date on a new GTA Online.
A wait wouldn't be new. GTA 5 came out on September 17, 2013, and GTA Online followed on October 1, two weeks later.
So on November 19 it's you, Jason and Lucia. If Rockstar announces an Online date, this page gets updated with it.

Watch us check it
Sources
Until launch this comes from pre-release previews and interviews. We re-check every verdict against the real game after November 19 and note any change here.