Sure, it is possible.
For older 4200, they can connect to external instruments on gpib or LAN (raw socket).
The newer 4200A-SCS adds usb and VISA for connection to external instruments.
The scope you mention has both LAN and USB.
For the software environment to send commands to scope and read data back, a library would be written using KULT tool. Depending on your overall objectives, the code you write with KULT can also interact with the SMU, CVU or PMU hardware in your 4200/4200A. The compiled library is run from KITE or Clarius UTM (user test module). KXCI can also call user libraries.
Take a look at example KULT libraries on your system. Ones for temperature control or for external LCR meter can give you an idea of interaction with external instruments.