If you have a separate physical partition to copy your installation media to, you could do that and modify Grub to Kickstart on boot.
install harddrive --partition=sdb2 --dir=/path/to/installation-media
title Reinstall CentOS 6
kernel /vmlinuz-kickstart ks=kickstart.cfg
You'll need to modify the values above (where appropriate) for your environment. The Kernel and intial ramdisk can be copied from the installation media (usually in the ./isolinux directory.) Note: I appended -kickstart to the filenames so that they stand out in a directory listing.
Last, set the default Grub entry to this one and reboot. (Count the instances of title, starting from 0.)
I can't stress enough that you should test this locally in a VirtualBox VM or the like before trying it on a colocated system.
For more information:
Starting a Kickstart Installation