Arduino Nano use SPI pins as I/O pins? and still be able to do ISP?
Yes, you can use SPI in your sketch just as you like. The programming over ISP is triggered by resetting the microcontroller. That means, that when trying to program over ISP your sketch (which configures the SPI hardware for use) doesn't run. The programming is starting at a stage, before the sketch runs, thus the sketch cannot interfere.

By the way: The same is correct for programming over Serial, though for a different reason. Programming over Serial is done by the bootloader, which runs before your sketch.