Next season I won't get Arsenal as one of the strongest candidates in the Champions League, but they deserve to be among the ones that will compete for tickets to the final. Regardless of how long Arsenal have been absent from the Champions League, I think Arsenal can be expected to be one of the teams that will provide great competition next season.
I agree Arsenal can't be said to have a winning mentality yet, but things can change quickly if Arteta is able to increase the confidence of his players over time. Manchester United, Newcastle, Arsenal and Manchester City will represent the Premier League in the Champions League, but only two of the four above seem likely to qualify for the quarter-finals.
I think the absence of Arsenal in joining UCL for a long time, won't have any impact on their performance. It is all about the players' mentality and ability, Arsenal seems not ready for this. They have many skillful players, they are young and very convincingly. But they have no experience in UCL, they have no mentality to maintain good performance till they reach the final round. TBH, I expect much on Arsenal but not sure they will reach the final. I still believe Man City, Bayern Munich, Barcelona, or Inter Milan which have the chance to reach the final. Commonly, the teams which have good experience in UCL that can compete for the title in the final round.