Yes, and no. If all your types are known you can compile to (even small, in theory) binaries, but in general you can’t! I mean, in general, the binary needs to include the compiler (and/or interpreter).
Think of the function:
mul(a, b) = a * b
Do you want to compile only for the integers, or floating point, or string concatenation or the infinite possible types, as Julia is generic? In general you could @eval at runtime, and solving this runs into the halting problem, theoretically not possible. Restricted Julia without being limited to being generic is still as powerful as e.g. C (you could e.g. type all your functions).