I tell you what's "unmitigated nonsense" - your assertion that the decline of the team's performance was purely down to the fact Pep was coming!
You have absolutely zero evidence for that.
If anything, knowing the greatest manager of his generation was coming could have acted as a motivator for those who wanted to be a part of it.
Certainly seemed to work for Bayern who had the best season in their history when the squad knew Pep was coming and the current manager was "keeping the seat warm".
In terms of Pellegrini's tactical acumen, I'll give you a quote from someone who worked with him on a daily basis while he was at City - "The only tactical changes he makes is he plays Kolarov at left back against Stoke because he's good in the air".