Who knows if when it add a new card like WS-X6724-SFP. do I need to turn off the switch or it can be added without turning off the switch?
You mean you don't trust us :-)
If it is a critical switch i would still do it out of key production hours.
Further to the good information by Jon, don't too concerned if you notice that the diag light remains red for some time, it does take a while for the card to boot and complete POST.
If you connect via console when you insert the module, you should the POST message logged to the console when completed and the status should change to Green.
Incidentally all ports will be disbled.
You do not need to turn off the switch. The 6500 supports OIR (Online Insertion & Removal) and for that price it should :)
You should be fine with this.