Yes, you do, Peachey!
Since I see that you are familiar with french, most of the time "mica" is used as intensifying adverb as in the french negative constructions like "ne... point".
It might be interesting to look at the etymology of the word, as well.
It probably has its roots in the ancient greek word μικρός (mikrós = little), which apparently had "traveled" through Europe till it arrived to Portugal with the meaning of "powder/pulverize". (vb. migar)
Thus, when you say "non è mica veer", its "intrinsic" meaning is "it´s not truer than a fleck of dust." = "it´s not true at all". better example: "non vedo mica nessuno" = "I do not see (even a fleck of dust of) anyone [at all]".
To the perfect explanation by Fede, I would like to add it is also to express astonishment or dismay: "non mangerai MICA quella m***a!!!" = "SURELY you are not going to eat that ****!!!"