Kind of. Imagine an "inline" function which isn't static, which (for whatever reason) the compiler decides not to inline the function at some call sites. It generates a function and calls it.
The compiler has to assume that this could happen in multiple compilation units. So in general, each compilation unit will have its own copy of this function. The One Definition Rule, however, states that there must be only one copy. This means that the linker has to discard all copies but one.
What this means for the optimiser is that every generated version of that function must be the same. That doesn't mean they have to have identical code, of course; the compilation units could be compiled with different optimisation settings. But they have to do the same thing, and hence they have to satisfy the same ABI.
There is one similarity: If the compiler optimises away all references to an inline function in this compilation unit, then it doesn't need to generate a definition for it in this compilation unit.
Great... I'll stick with "static" instead of "inline".
You should use whatever matches your intention. :)