Programming nRF24LE1 with the AVRISP
If two devices share the same instruction set, that is no guarantee of compatibility. They may be completely different in terms of program memory space, peripheral memory map, programming interface, etc. The ISA implementation might even be quirky, but that's another story. For now, you have two concerns: 1) compiling code and 2) programming the device. 

First, you can't use AVR Studio to compile because it only support AVRs, as you can see from the list. (I don't know if earlier versions have 8051 support.) From googling, it appears that you could use sdcc/makefiles, sdcc/Eclipse, or one of the many for-pay 8051 development environments.

Second, AVRISP does not support the Nordic part. AVRs and the Nordic part both look like SPI Flash for programming purposes, actually, but the Flash command set is completely different. In theory you could use the AVRISP hardware, but you would have to write your own software or modify avrdude appropriately; not a walk in the park. From some googling, users of this chip have written their own programmers, using various microcontroller platforms. So you appear to have the option of implementing your own programmer, or purchasing Nordic's.