I think the absence of Arsenal in joining UCL for a long time, won't have any impact on their performance.
It will do have impact on their performance. It is very rarely to see a club get success in their first season return to Champions League. It is some barely seen successful comebacks from some clubs but usually they will struggle with their first one or two seasons there.
Napoli, Inter Milan, AC Milan failed to go through Champions League group stage before they gained bigger success in later seasons. If you want to find a club from Premier League, it's Manchester United and Manchester City. Manchester City needed many seasons to slowly improve their performances in Champions League.
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.
They have skillful and strong mental players but they surely lack of experience in Champions League. It will impact their performance when facing with biggest clubs from different European countries and leagues. Playing in Champions League means Arsenal players will have to play with many different tactics from different clubs and leagues. It is very different from playing with clubs from Premier League that somewhat have a common philosophy.
Arsenal can go to a first knock-out phase but it's hard for them to go farther.