Seems a bad idea even as syntactic sugar, except for the case of using PyCall (when the target language is loosely object oriented).
If you prefer object oriented dispatch, many languages offer it. With strong typing, optionally as Julia provides, OO dispatch can off make class inheritance very difficult. I realize the OP has no issue with multiple dispatch and wants to preserve it and the syntactic sugar would rarely, if ever interfere with it. Since multiple dispatch is expressed with function call syntax, Julia should stick to that. While I wouldn't want Julia to go too wild down the functional programming path, the key benefits of FP that Julia provides--namely, multiple dispatch, 1st class functions, and closures--are really great and handily fit a language with a more imperative style. In Python (I still love Python), x.f(y) is really just syntactic sugar for f(x,y). It almost seems silly to have it at all. And since Julia is even less OO than Python, which is to say not at all then it seems almost misleading to mimic the OO syntax since OO is definitely NOT what is happening under the hood. While I realize the OP is not really asking for it, it is still worth pointing out that there seems little benefit to going down the OO path.