LT3029 regulator for arduino mega
You say LT3069 in the title, but LT3029 in the text. I assume you mean LT3029 since the LT3069 seems to be rare, at least as a regulator. 

The answer is in the datasheet. No it does not work with zero external components, it needs at least six total components for a single output. It's also a pretty unfriendly part to work with unless you have a premade PCB or proper equipment (DFN with 0.45mm pitch or MSOP with 0.5mm pitch- and it's expecting a ground plane for heat dissipation). 


  All measurements
  were taken in still air on a four-layer FR-4 board with 1oz
  solid internal planes, and 2oz external trace planes with a
  total board thickness of 1.6mm.


But you don't need it- according to the official web page for the Mega:


  Input Voltage (recommended)   7-12V


So, 12V is within the recommended range. The 2A is sufficient. The microcontroller board will draw what it needs (and no more) when connected correctly. You only need to worry about the current if you plan on drawing a lot of current from the I/O pins or from the internal regulator. 

Edit: LOL I put that "when connected correctly" in there before seeing your comment on your classmate. It's kind of important.