No. For all the reasons @kaz-k mentioned. Once in a while it may be possible to do this between two models that are just a generation apart and otherwise share the same hardware with the only difference between Logic Boards being a CPU, but even then it is rare. About the only thing that usually works is installing a Logic Board for the exact same model year which has a faster CPU. For example if you had a Logic Board with an i7 CPU for the same exact model as your laptop, then you could install it to upgrade from an i5 CPU (same if using a Logic Board where the i5 CPU is 3.1 GHz instead of 2.5 Ghz....again assuming the Logic Board is made for that exact model.
I know the 2013 & 2014 models share a lot between them, but I don't even know whether their Logic Boards can be swapped between them. The 2015 model had a lot of hardware changes so the parts for the 2015 can only be used in a 2015 model (there may be some minor exceptions such as Speakers, but I don't believe any of the other major components are compatible with even a 2014 model).
Any legitimate part seller will clearly state which exact models any particular part is compatible. If the seller does not clearly state exact models, then I would not deal with that seller since those details are really important.