The 16F628A does not have a built-in hardware debugger.
So what Microchip said is true if you are using one of their programmers as a debugger.

And anyone that said you can debug a 16F628A with MicroCode Studio was also correct, because MicroCode uses software debugging via the USART and doesn't need a hardware debugging module.

You can use the serial communicator in MicroCode Studio to verify operation.
Connect to the port at 19200 baud and send a lowercase 'h'.
If everything is working properly, it will respond with a 6 digit hexadecimal number.

Make sure you have compiled the program using the "ICD Compile" or "ICD Compile Program" buttons.