Vietnamese is a tone language, and it is written in a Latin script (with a number of accent marks). If it can be done with Vietnamese, it can be done with Chinese. For that matter, lots of tone languages are written in Latin scripts.

The problem with Chinese is not that it is a tone language (not absolute pitch, but relative pitch); the problem is that there are many regional dialects with different tone systems, and other pronunciation differences as well. Not that that's a real problem; English has lots of dialects with very different pronunciation systems, and it's written in a dialect-agnostic way.