Interesting
Pigs
are smarter than dogs, so I don't see why it wouldn't work.
It doesn't have to be a huge effort to start training, just start taking a board into the pen with you at feed times and use it to shuffle her round - she'll soon get the idea. Don't go for any kind of intensive work til after she's weaned the piglets, she'll be too focused on them to concentrate I think (I've never train a sow who has a litter, so maybe I'm wrong though)
The stick is only to move her along (important in the show ring) but if you're moving her round at home she'll probably walk without the stick and you'll just need to give her a couple of taps on the rump to get her moving if she does stop. Keep the board down below her eye level and just at the side of her head, keep up with her as she moves so you can 'steer' her and away you go
Oh and if you do decide to train them to the whistle, you've GOT to post a video, that would be great