No, you can't run code from the SPI memory. You can write your own code to code from SPI memory into a RAM memory that is shared with the code space. But it will not be fast.

You can not directly read/store variables there either, but you can write a library to store seldom used data there, and read it out before use.

An example: A processor running basic may store a large number of basic programs in the SPI memory.

A large menu system may be stored in the SPI memory, and then retrieved one menu at a time when needed.

A huge - but seldom used - array can be stored in the SPI memory, and then accessed by a get_array_element() function.

Your question can be translated to the PC architecture: Is it possible to use the HDD as code or RAM memory? You can swap data out (making the PC slower), but you can't run any programs directly from the HDD. The big difference between a PIC and your processor, is that the PC have a memory management unit (MMU) which makes it possible to fake a larger memory - your application need not see (other than as delays) the page faults that results in data being transmitted to/from the HDD). With the 8051 architecture, you must manually call functions to swap data to/from the SPI memory.