Can the PPK-BL600 programming jig be used to test the functionality of a programmed BL600 module?

Answer

No. The PPK-BL600 only has RX/TX/CTS/RTS lines connected and therefore cannot go into autorun mode. In other words, there is no way to test an autorun script on the BL600 module via the PPK-BL600. 

For more on the PPK-BL600 programming jig, see the following Quick Start Guide:  "Using the PPK-BL600 Programming Jig."