In general, investigating this features is mostly trial and error, because [`Compile`](http://reference.wolfram.com/language/ref/Compile.html) is a pure kernel function that resists inspection by `PrintDefinitions` or `Trace`. Therefore, the only reliable source of information are the one example from the documentation and trying things out. What follows is list of rules extended from my comments.

What can be inlined by `"InlineExternalDefinitions" -> True`?
--------------------
In principle, basic *own values* (see [`OwnValues`](http://reference.wolfram.com/language/ref/OwnValues.html)) created using [`Set`](http://reference.wolfram.com/language/ref/Set.html) can potentially be inlined by `"InlineExternalDefinitions" -> True`.

    ext1 = 1;
    ext2 = Pi;
    ext3 = #;
    ext4 = Sin[x];
    ext5 = Compile[{x}, Cos[x]];
    ext6 = #^2 &;
    
    cf = Compile[{{x, _Real, 0}},
      ext1*ext2 + Nest[ext3 &, x, 10] + ext6[ext4*ext5[x]]
      , CompilationOptions -> {"InlineExternalDefinitions" -> True}
      ]
    
    Needs["CompiledFunctionTools`"];
    CompilePrint@cf

What can't be inlined by `"InlineExternalDefinitions" -> True`?
----------------------
Everything else, especially `OwnValues` created by `SetDelayed` and [`DownValues`](http://reference.wolfram.com/language/ref/DownValues.html), can't be inlined by `"InlineExternalDefinitions" -> True`.

    ext7 := 1;
    cf2 = Compile[{{x, _Real, 0}},
      ext7*x
      , CompilationOptions -> {"InlineExternalDefinitions" -> True}
      ]
    
    CompilePrint@cf2


    ext8[x_] := x;
    cf3 = Compile[{{x, _Real, 0}},
      ext8[x]
      , CompilationOptions -> {"InlineExternalDefinitions" -> True}
      ]
    
    CompilePrint@cf3



What will be inlined?
---------------------
Which `DownValues` will be inlined by `"InlineExternalDefinitions" -> True` is decided by the algorithm of `Compile` and is therefore hard to predict. It has even [changed between version 9 and 10](https://mathematica.stackexchange.com/questions/54694/in-compile-inlineexternaldefinitions-doesnt-work-anymore-in-mma-v10-like-in-v). 

Wolfram Technical Support: "According to the developers, nPara is not inlined because Mathematica is making the conservative assumption that nPara might change in the future."


How to force inlining?
----------------------