No! Thanks a lot.

So basically, the logo won't always look the same color depending on the type of paper?
Usually, if you specify a Pantone color, the printer will use
whichever type of Pantone ink (coated or uncoated) appropriate for that paper the exact same ink on either coated or uncoated paper. That's just standard industry practice. So if you specify "Pantone 295" and are printing on an uncoated paper,
the printer will use Pantone 295 U. If you are printing on a coated paper, the printer will use Pantone 295 C the paper will absorb more of the ink and end up looking a lot different than the same ink on coated paper.
CORRECTION: As PrePressAcrobat helpfully pointed out, the above explanation was not technically correct. The ink is the exactly the same whether it's printed on coated or uncoated and only changes due to paper absorption and brightness. The offending text has been struck and more accurate edits added. Sorry for the confusion.
Now, looking at the swatch books (if you have the luxury of both uncoated and coated swatchbooks handy), and you are happy with the correspondence between Pantone 295 U and Pantone 295 C (in other words, if they look the same side by side, or at least close enough), then you'll probably have no problem with the printer
swapping coated for uncoated ink with the same number printing the same color on either type of paper.
But, if you
don't like the correspondence between 295 C and 295 U, then you may wish to search for and specify different colors for uncoated versus coated papers, say 295 on uncoated, and 2965 on coated.
Here's a slight wrinkle when it comes to the paper itself: Not all white papers are the same color temperature. Some are slightly bluer, some a bit yellowish. This is measured as paper "brightness" and it can subtly affect the color of the ink. I don't think in your situation this will be a big issue if you are selecting a white paper, but beware that if you print a Pantone color on an off-white paper (cream, or "natural white" or any manner of paper colors out there), you may be surprised because the paper color
will definitely affect the ink color.
Make sense?