Of course it will work, why wouldn't it? Can you put RAM in a ram slot and a soundcard in a PCI slot and have them both work?
My friend told me that my motherboard should have PATA/IDE controller in order for SATA hdd and IDE optical drive to work?
I have no idea what your friend is trying to say. You need a PATA controller for the IDE channel to work, and a SATA controller for the SATA ports to work. The PATA controller won't work on a SATA drive. Yes you have a PATA controller, its how you use your current disks.
The only thing you have to worry about is changing the jumper on your DVD drive. It will have to get changed to Master. You might also need to adjust your boot options in the bios.