Facing Arsenal in a challenging match, it seems that a defeat for Chelsea could be a somewhat accepted outcome for Pochettino. This is due to the fact that Arsenal is currently a formidable team, as evidenced by their recent victory over Manchester City. It demonstrates that Arsenal is truly at the peak of its performance early in the season, with only a 2-goal difference separating them from the current league leaders as they sit at second place.
However, what may not be forgiven is if Chelsea suffers a loss to Brentford on October 28. Should Chelsea indeed face defeat, Pochettino's position might come under some threat, as he could be perceived as failing to make Chelsea competitive in the EPL. While Pochettino is likely to be given more opportunities in the weeks to come, his position will, at the very least, be in a somewhat precarious state.
Even though the performance conditions of the two teams are very different at the moment, but I am sure Arsenal will not easily secure full points when they face Chelsea at Stamford Bridge. No one doubts Arsenal's abilities so far because they are still quite consistent until the eighth week. But I predict the match will end in a draw, the reason is because Chelsea has shown good results in the last three matches and the match will also take place at Stamford bridge.
It is still too early to say that Pochettino has failed to make Chelsea more competitive in the EPL because they still have quite a lot of matches to play. Usually the teams currently in the top 10 will lose consistency in the second half of the season and only a few strong teams will survive. So there is still a chance for Pochettino to show team improvement and they will still be chasing the top five this season.