Absolutely.  Per MSDN (http://msdn.microsoft.com/en-us/library/d93tkzah.aspx), 
This method performs a word (case-sensitive and culture-sensitive)
  search using the current culture.
So you may get different results if you run it under a different culture (via regional and language settings in Control Panel).
In this particular case, you probably won't have a problem, but throw an i in the search string and run it in Turkey and it will probably ruin your day.
See MSDN: http://msdn.microsoft.com/en-us/library/ms973919.aspx
These new recommendations and APIs exist to alleviate misguided assumptions about the behavior of default string APIs. The canonical
  example of bugs emerging where non-linguistic string data is
  interpreted linguistically is the "Turkish-I" problem.
For nearly all Latin alphabets, including U.S. English, the character
  i (\u0069) is the lowercase version of the character I (\u0049). This
  casing rule quickly becomes the default for someone programming in
  such a culture. However, in Turkish ("tr-TR"), there exists a capital
  "i with a dot," character  (\u0130), which is the capital version of
  i. Similarly, in Turkish, there is a lowercase "i without a dot," or 
  (\u0131), which capitalizes to I. This behavior occurs in the Azeri
  culture ("az") as well.
Therefore, assumptions normally made about capitalizing i or
  lowercasing I are not valid among all cultures. If the default
  overloads for string comparison routines are used, they will be
  subject to variance between cultures. For non-linguistic data, as in
  the following example, this can produce undesired results:
    Thread.CurrentThread.CurrentCulture = new CultureInfo("en-US")
Console.WriteLine("Culture = {0}",
   Thread.CurrentThread.CurrentCulture.DisplayName);
Console.WriteLine("(file == FILE) = {0}", 
   (String.Compare("file", "FILE", true) == 0));
Thread.CurrentThread.CurrentCulture = new CultureInfo("tr-TR");
Console.WriteLine("Culture = {0}",
   Thread.CurrentThread.CurrentCulture.DisplayName);
Console.WriteLine("(file == FILE) = {0}", 
   (String.Compare("file", "FILE", true) == 0));
Because of the difference of the comparison of I, results of the
  comparisons change when the thread culture is changed. This is the
  output:
Culture = English (United States)
(file == FILE) = True
Culture = Turkish (Turkey)
(file == FILE) = False
Here is an example without case:
var s1 = "é"; //é as one character (ALT+0233)
var s2 = "é"; //'e', plus combining acute accent U+301 (two characters)
Console.WriteLine(s1.IndexOf(s2, StringComparison.Ordinal)); //-1
Console.WriteLine(s1.IndexOf(s2, StringComparison.InvariantCulture)); //0
Console.WriteLine(s1.IndexOf(s2, StringComparison.CurrentCulture)); //0