Broadly speaking this is correct, but there are words that see more common usage in one dialect over the other, so reading a sentence written with chinese characters could inform you which dialect it is meant to be read in.

An incomplete example of this for someone who is more familiar with english would be detecting whether the author of a sentence is british or american based on the usage of different words with the same meaning e.g. torch vs flashlight.

Both dialects/variations of english share the same written alphabet but still maintain distinct differences that can be detected on paper based on key word usages (or even spelling in this case e.g. metre vs meter).

I say this is an incomplete example because the spoken variations between english dialects are generally not wide enough that one is incomprehensible to the other, but I think it helps demonstrate my point to people who are more familiar with latin/germanic languages. There are also some dialects of chinese that are relatively close wherein speakers of one can understand speakers of another. But in the case of cantonese and mandarin specifically, they are relatively dissimilar when it comes to how they are spoken.