Horcruxes, the Prophesy, where Dumbledore goes, and other secrets

[steven1965aaa]

No: HPFGUIDX 154116

The portraits of the former headmasters are privy to everything that 
goes on in Dumbledore's office.  When Dumbledore and Harry spoke after 
seeing Slughorn's memory, one of them even used an ear trumpet to make 
sure he heard everything.

I remember (I think from OOP, IMR) that the portraits serve the 
current rightful headmaster of Hogwarts.

Therefore, wouldn't McGonagle be able to find out where Dumbledore 
went when he left Hogwarts,about the prophesy, Horcruxes etc., all 
just by asking the portraits the right questions?