Using the circuit from Tip #2 with the LEDs on the ICSP pins I get a wrong chip selected error. On the 12f683 I have GP0 on pin 7 and GP1 on pin 6. Pin 4 is pulled high with a 500 ohm resistor. It seems the programmer is only picky about pin 7 being used.

Tip #2 should be what you need.
http://www.picbasic.co.uk/forum/cont...ips-and-Tricks

How can I connect LEDs and the ICSP header on the same pins?

As usual, your thoughts are surely better than mine.