There might be similarities, but it depends on the evolution of the syllable in that particular dialect.
Mandarin is actually a wacky dialect as these things go. Cantonese, Shanghainese and Taiwanese (Minnan) are more conservative. Get somebody to read you a couple of the “300 Tang Poems” in Taiwanese sometime, if you can – it’s much easier to imagine how they would have sounded back when.
There were also some phonetic changes related to what happened to the “entering tone” of Ancient Chinese. Mandarin really developed along a different pathway, which is why the other dialects mostly have more tones. You can also see Mandarin dialect areas with just 3 tones instead of 4, for example, in some places in the ML (so I was told in grad school, at least – I haven’t been there personally to check it out, I’m not that bad!!)
Now, as for details – don’t ask me, please! I had to memorize and regurgitate the process of consonantal evolution from Archaic Chinese through Ancient Chinese to Modern Mandarin for my qualifying exams, and I promptly did what the Taiwanese students do: “huan gei lao shi” – gave it back to the teacher (i.e., forgot it).
I find that having some general idea about the sounds of Ancient Chinese helps a little bit in the area of Minnan, but the most facilitating way to handle Minnan for me is to pretend I was drunk speaking Mandarin.
Sorry, Bri – only a half-serious answer, best I can do on a Sunday!