I've been playing with this so I'll jump in.
A scale 3/8ths thick will almost always warp when soaked and dried.
Anything thinner will be worse I'm sure.
You can stop some of the warping by placing it under a flat, heavy weight when drying with hardener. Make sure it is completely dry before removing from the weight.
WSSI does a great job and their results are much better than home brewed wood hardener. Most of the pieces I have sent them (3/8ths, 1/4, that range) came back with some curl. (less than my attempts) They will tell you to have an oversize piece treated to take this into account. This isn't a slam against them. It's just the nature of wood.
I have had blocks warp, twist in the 2"x2"x5" range although this is much less apparant and frequent.
If I had thin scales to do, I'd brush on the hardener lightly and let it dry, several times. I'd also keep it under a weight when drying.
On a side note: I've been testing products called Pentacryl and Polycryl. The polycryl is marketed as a wood hardener for soft wood. I've tried it on punky spalted maple and it does harden it some what but it is not what I would consider hard enough for a knife handle. I have sent some off to WSSI to treat for comparison.
Pentacryl simply won't work on soft or punky wood. After a lot of trials, I now have my doubts about this stuff too.
Minwax wood hardener does make punky or soft wood a lot harder but does not fill the pores of the wood with 'poly' like the WSSI treatment does. I am going to try a 'triple quench' (us stock removal guys can throw that around too

) and see if that makes a difference.
WSSI is good at what they do. They will charge you $12/pound for small lots for their goop and seems to be the cheapest way to go after fooling around with all the hardener and other stuff I have been.