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.
Well spoken, however sometimes is good to give up something in other to accomplish other things, so in the case of Arsenal they have the performance to compete on the champions league but it will do them more good if they should only project all their focus on the premier League because that's were they have more chances of wining than champions league because even if they managed to draw with Bayern Munich doesn't give them the ticket of wining the champions League, so I believe Arteta should be able to channel there interest more on the premier League.