Here’s what it does for you.
It will make squeeky whistles more stable. It takes out that squawk or buzz that you sometimes get on some whistles. I have a Hoover whitehead on an Oak body that was impossible to play due to this problem. Three applications of hairspray fixed that.
What it won’t do is fix excessive breathiness. At least that’s what I’ve found on a Kerry Songbird (POC).
I’ve also found that the tweak works best when the spray goes into the chamber and also the windway. I’ve been wiping it off the blade (labium) and getting good results. I haven’t proved it yet, but I suspect that coating the labium would change the sound too, for better or worse.
Others may be able to add to this.