Maybe, maybe not, but the situations aren't exactly the same anyway and the comparison is a bit forced imo to begin with. They signed players mostly for immediate success, players considered ready to play at the very top right away - Thiago Silva, Chilwell, Ziyech, Werner and Havertz all for massive money/monster wages.
We've changed practically the entire XI in the space of 12 months, ripped the squad up on top of that, and almost exclusively bought U23 players that have never played at the top level. And we have the youngest squad in the Premier League. Even with all of those differences to Chelsea, I expect Arteta won't last beyond Christmas if he doesn't get this team going.
I think Arteta should definitely be given that time. It would take a disaster - a string of losses and the players downing tools, for example - for me to think it would be right to fire him before then.