Possible to store variables directly in EEPROM?
Writing and reading EEPROM is possible to do without a library. Take a look at the datasheet of the ATmega328P to find an example: On page 25 / 26 there are example codes for reading and writing both in assembler and C. They do wrap it in a function but as I said in a comment if you only have place in your code where you would like to access EEPROM you can put the code there without duplication. These functions write and read one byte at a time, so if you want to store larger datatypes (a 16-bit integer for example) you already need to call the routines more than once.

Note that the EEPROM has a limited life cycle of at least 100,000 write/erase cycles (cells must be erased before they can be written, reads are unlimited) and it is considerably slower than SRAM (typ. 3.3 ms for writing a byte). You also need to make sure no interrupts interfere with the write process.

However, in the sense of the question it seems this is not what you want: You cannot just create a global variable and have it magically being written to EEPROM.