From a code point of view no.
From a UI point of view (which is how your question is phrased) I'd say yes.
The reason I say this is that although it's specified, many people read "mandatory" as "significant" (how many people skim web forms only filling in the smallest amount of data?).
If the specific value in the field is important you may wish to use the mandatory * to show that it shouldn't just be skimmed over but that the user should give it some consideration.
Plus for pedants (and we're all computer programmers so that should be most of us) surely we should be saying it IS mandatory so should be marked as such, regardless of the UI component being used.
This may also protect you from the change down the line when someone says "let them pick any value and replaces it with a text box".