Since @MTSan already gave an excellent answer, I thought I would throw a twist into the discussion.
While you asked whether or not the shape of the drinking vessel would impact the coffee's flavor, this leaves out an important aspect of the cup you're drinking from: it's color!
While there are a few different sources out there, here's one research paper on the subject I found.
In it, the authors note that:
Both experiments demonstrate that the colour of the mug affects people’s ratings of a hot beverage...
...it is possible that colour contrast between the mug and the coffee may have affected the perceived intensity/sweetness of the coffee."
While all such research should be taken with a statistically significant grain of salt, it's still food for thought.
I hope my slant adds to this Q&A! Comments and edits are encouraged.