If a SoC is given more memory then it is able to use, how does it deal with that?
Say it can only use 2GB's, and is provided 4, does it only use half,
  or not use any of the ram?


A "generalized" microprocessor or SoC has typically three buses and the relevant one to this question is the address bus. If it has a 16 bit width (like the 8085) then it can only "talk-to" 65,536 (\$2^{16}\$) memory locations. This means you cannot force it to be connected to more. Buses on an 8085: -



If you have some RAM that is bigger than that implied by an address bus of 16 lines then you should ensure that unused lines (on that memory) are tied to either logical 1 or 0.