I don't think there's currently any way to do that (ignoring case) using the .NET API, although it certainly would be possible using the REST API (meaning it's a very reasonable feature request).

For now the easiest way would be to mold your index a little bit to include an additional field with the value of the property already lower cased. In other words, add a property to your class(es) with the value as lowercase, or include an extension method, and then sort by that.