Can I put a 2011 Logicboard in a 2012 MBP?

For reference here's the IFIXIT logic board replacement guides:

• MacBook Pro 13" Unibody Late 2011 Logic Board Replacement
• MacBook Pro 13" Unibody Mid 2012 Logic Board Replacement

While these two logic boards are very similar there are a few differences which might impact you. The heatsinks are very different so you can't swap them out. In addition the RAM modules are different:

• 2011 models - 204-pin PC-10600 (1333 MHz) DDR3 SO-DIMM
• 2012 models - 204-pin PC3-12800 (1600 MHz) DDR3 SO-DIMM

Now you stated the 2012 system has juice spilled into it. I'm not sure if this exercise will get you a working system in the end. The problem here is you likely has a messed up keyboard & trackpad which will need to be cleaned or replaced.

Lastly depending on on the condition of the 2011 model you have, it might be worth getting the uppercase replaced and then transfer the display from the 2012 over (if the 2011 is in sad shape). It would be the least risky way to get things going here.