8 bit MCU with 12 bit ADC, possible?
There is absolutely no problem in interfacing a 12-bit ADC with an 8-bit micro. The one you show has I2C interface, so it's a bit easier if you pick a micro with I2C bus support. Atmel calls theirs "Byte-oriented 2-wire Serial Interface" because of Philips' IP rights, and the Atmega processors have such an interface in hardware. 

It is common to use more than one byte to represent data. If you were programming in C you might use an int, long int or even a float. You can write code in assembler to deal with 8, 16, 32 or 256 bit numbers if you really want (limited by memory). 

Simplicity of coding is highly dependent on what exactly you are trying to accomplish, and what your tools and experience are. If you are using a compiler, the details of the hardware are mostly hidden from you so it doesn't much matter (speed could be a bigger factor).