No, the PICs like most other devices have a built in ID number that identifies the manufacturer and actual device, it isn't the same number as written on the package. The code 2A20 is the internal code for the 16F1783 so yes, it can be programmed with a Pickit2 as long as the new device file is used (post #2). The 16F1783 was released after the Pickit2 so it never appeared in the original device file shipped with it. If you overwrite the device file with the newer one it will add several newer devices including the 1783.
Brian.