I don't think that's accurate at all. We signed Monreal while we had two left backs who wanted to stay. We signed Ozil while we had 3 players who played at no.10, there's various other examples.
I think if he has the chance to sign a player he really rates, he'll go for them regardless of who he might upset. I don't know if Cech falls into that category, but if Benzema become available I don't think he'd worry too much about upsetting Giroud, Welbeck and Theo.