What you are saying is true because it has happened to Arsenal last season when they lost the opportunity they had on wining the premier League last season to Manchester City and they almost repeated the same thing again this season if not that they were able to regain there performance when the league is still on, however I don't think Arsenal playing on the two leagues will affect them because right now there focus is not really on the champions League because they know fully well that there are more quality clubs on the race for that trophy, so there interest now is on the premier League.
Most likely, clubs will always give priority to the Champions League, but the Premier League is also a very respected championship and I would not be surprised if Arteta wants to become the champion of England and sacrifices the Champions League for this. Still, there is Real Madrid, with whom it is very difficult to compete, although you can of course try to win both tournaments, but Arteta understands how difficult it is, even Bayern, which now has a lot of problems, looks like a very formidable opponent.
Sometimes the Champions League and Premier League have almost the same level of difficulty. Where in the premier league, Arsenal also competes with Liverpool and Man City. But I am sure that if Arteta can focus more on the Premier League then winning the Premier League title this season can be achieved. But I'm sure Arsenal management will prioritize both. Because after all the Champions League is the highest competition in the European League. So it could be more important than the Premier League if you consider the reputation of a club. but it is very difficult to be able to divide focus on two equally difficult competitions. But it is not impossible to do, just like Man City last season, which also divided their focus into all competitions and everything was successful.