You could try it and see if it works. It's been over a year since I did HP and mine was always gloppy. It's just my opinion but I think it might be too thick to pipe. But I might be wrong since I'm basing this on my experience with HP.
Whipped soap can be piped onto other soaps and bath bombs. Have you considered using a whipped batch instead?
I don't think the heat would be an issue since you'd be wearing gloves. You could try to put some in a baggie with the tip cut off and experiment to see if it would work. I really don't know but it's an interesting idea. Now you've got me intrigued on whether it would work or not. I usually don't do big enough batches for HP. My crockpot is too big so I just make CP.
Whipped soap is very easy. agriffin posted a recipe and instructions if you'd like to try it.
I didn't try HP like you asked, but hopefully there will be some some useful info to extract from my experience.
Not long ago, I got curious about whipped soap and thought the best idea is to practice on a rebatch: simply melting a couple of old bars with added water (I tried this on few recipes with a hardness around 40-50).
Obviously, the melted soap was too thick to put through a piping bag. So I just thought to add a little more water. The water got it thinner so it could be easily whipped and then piped.
I am far from being a piping bag expert, so I had a lot of trouble getting the desired thickness. Sometimes I would add too much water and it got too thin. But mixing it some more got it hard again.
The result wasn't perfectly smooth (like butter cream), it was a bit rougher, maybe like a meringue that you beat really stiff. But ok for a first try.
By the way, I don't know how you would "glue" the frosting to the cupcake.
I think you have to roughen the surface of the cupcake. I didn't roughen the surface when I made cupcake bath bombs and the whipped soap only adhered for a short time and then fell off. There's tutorials about piping soap onto cupcakes but I haven't tried again.