Let's be fair here. PP must receive hundreds of emails daily and although each email may be very important to the sender, said email may rate far lower on her list of priorities, and quite rightly so.
No.
You are essentially defending either her laziness in replying, her unwillingness to delegate to an underling, or her inability to manage her time and resources. All completely unacceptable in a senior manager.
Of course I don't expect an immediate response to every single message that comes into her Inbox. The volume must be enormous. And occasionally emails go missing, are accidentally deleted, whatever. Fine. But we're not talking about the odd delayed response here. More like a total lack of respect she has shown over and over and over again by completely ignoring multiple attempts at communication. I would challenge you to find very many who don't have a story about trying to contact PP - she's infamous.
As BigGeordie says. It's her job. If not to personally answer, to pass along to the relevant department. If she can't do it, surely she has underlings to assist.
About the best I can say is that at least she isn't an aberration. The horrendous lack of comms seems to be a company-wide cherished tradition.