No. That's not at all the point of the Uno's ICSP header. The purpose of the Uno's ICSP headers is to facilitate programming the microcontrollers on that board. You can simply plug any AVR ISP programmer into those headers and all the necessary connections are made.
But that is for the Uno's microcontrollers as a target. When you use the Uno as a programmer, you can not just plug an IDC cable into the ICSP header. That would make a connection between the Uno's reset pin and the target's reset pin. You need to connect one of the programmer's IO pins (pin 10 by default) to the reset pin on the target. You can find some projects where people built a custom cable with a lead running off for that reset control pin. Here's one from Nick Gammon: