It should work. You mean she doesn't even twitch an ear? It's hard to say if she hears it or not. She may, but doesn't care to respond. LOL.
Try this: Call your dog to come the usual way you do if she is obedient to the recall. (if not, work on that. You can use a long line if necessary) Right after you call her, blow the whistle. In other words, pair the two types of cues together. Give a high value treat when she gets to you. After you've done this for a few sessions......few days, call her to come, whistle a couple of times, then drop the verbal cue or whatever your existing cue is and just try the whistle.
Don't ask her to come from a long distance away. Start out making it easy. Normally, when you call her, are you facing her? Or do you call her and stand in various positions? Will she come if you're back is turned to her and you give your cue? If so, incorporate that in too. Test her out. See if she is coming to the whistle when she can't see it or see you put your hand up by your mouth.
I taught my Doberman and all my dogs to come to the whistle. But I've not used it for a while with my other dogs and they may have regressed with that. It's kind of neat and fun but whatever works best for you. It is nice if you have to call your dog in late at night or early in the morning so you don't bother neighbors. Let us know if it works out for you. Be sure and use tasty treats to let her know that it is a really cool thing.
Another thing you can do before trying to actually train her to come is simply find out if she hears it this way: (actually, this will teach her to come if she can hear it) Stand there and whistle while she's by you and right away give a yummy treat. Whistle, treat, whistle, treat over and over for about 5 minutes. Change positions, locations, walk to the other side of the room. Don't always do it when she's in the exact same position. Vary things. After you've done this for a while, blow the whistle and see if she looks at you like, "where's my treat!" Walk across the room, blow the whistle and see if she'll come running over to you to get the treat. Then try it outside where you have other noises and more space to rule out that she only hears a little air coming through but not the actual whistle.