I think it harming in the league is very overrated and an excuse used by teams that are too weak to do much in the league in the first place.
If we are too weak to compete for top 4 and EL it is most likely that the actual case is just that we are too weak to compete for the top 4.
These are the teams that Woolwich and Man United faced in the group stage: Eintrecht Frankfurt, Standard Liege, Vitoria, AZ, Partizan, Astana. There is no reason that my first team listed could not win a group with these teams without a single player from our starting 11.
In the knockout stage Woolwich, Wolves and United were matched with Olympaikos, Espanyol and Brugge and that was with Woolwich and Wolves failing to win their groups. Again 3 teams we can beat without having to use a ton of our first team starters.
Obviously with other Cups we are likely to have a few players overlapping but not enough that it should wipe out their stamina or fitness. When we have big EPL games coming up we can easily keep any players that are at risk at home and still be fine for the EL.
The biggest issue we have with top 4 is not the supposed drain that EL will have on us, it is the fact that we are at best the 5th best team in the EPL and maybe lower after the transfer window is done.