Go statically links to all Go libraries, and only dynamically links when interfacing with C code. (As of the last time I used it, a couple years ago; this may have changed since then.)
That doesn't really answer whether it can inline library functions. The fact that it statically links means it potentially could inline methods it finds in them but I don't think that it does currently since it appears that this inline functionality works when compiling source.
It can inline library functions, since, at latest, 1.4.2 (this is just what I happened to have handy on this computer). It's pretty easy to test by writing a package containing a simple function like "func Square(x int) int { return x * x }", compiling a main package that imports that package and calls Square, and then disassembling the executable to see whether it calls Square or inlines it.
