Some years ago I bought myself a "avrisp mkii" usb programmer.
Is it possible to use the Arduino developer/programmer software for this programmer?
I know you can use the ArduinoUNO board to program other Atmel devices but I wonder if I can use the "avrisp mkii" programmer directly on this Arduino software.
Yes it's possible. There are a couple problems you might encounter if you're using Windows.
If you have used Atmel Studio you will probably have the Jungo driver installed which is not compatible with the Arduino IDE so you need to uninstall that driver and install the correct one(libusbk or libusb-win32).