"Sorry," said Ron, wrenching Harry back out of the brambles, "but the name's been jinxed, Harry, that's how they track people! Using his name breaks protective enchantments, it causes some kind of magical disturbance --- it's how they found us in Tottenham Court Road!"
"Because we used his name?"
"Exactly! You've got to give them credit, it makes sense. It was only people who were serious about standing up to him, like Dumbledore, who even dared use it. Now they've put a Taboo on it, anyone who says it is trackable --- quick-and-easy way to find Order members! They nearly got Kingsley ---"
Harry Potter and the Deathly Hallows. Chapter Twenty - Xenophilius Lovegood
(Quote via mustard)
We know from the quote above what the jinx does when Big ol Vs name is uttered, we can also infer from the books how accurate it is.
We know that it will break protective enchantments we also see evidenced that it reveals the point of origin for Big ol Vs name it does not say which wizard or their exact location the death eaters have to seek them out.
This is evidenced in both Tottenham court road and when Fenrir and gang find them in the forest.
As for the muggle aspect or really the main aspect of this question. In what other part of the Potterverse have muggles been able to use Magic of any kind? The magical trace applied to underage wizard is not used on muggles which states that the ministry have no cause of concern where muggles possibly using magic is concerned.
We do know though that magic can be used on muggles but when placing the taboo would Big ol V care about muggles, would he not try to exclude them it would waste manpower he doesn't have. He is a great wizard and one could assume he would only be interested in "people who were serious about standing up to him, like Dumbledore".
We also do not know how big of an area the taboo affects i.e the ministry gets no information on the underage wizard trace for underage french wizards.
In conclusion I would say No the only possible reason I could see for Big ol V wanting to track Muggles who say his name would be there connection to Wizards who use his name but I also think he would underestimate their importance.