I have not, not have I ever had a synthetic boot resoled. I've never worn out the sole on a synthetic boot where the rest of the boots weren't trashed enough to get another pair. It kind of changes the game if it's your daily footwear, but the GoreTex is usually shot after a year or two and I've just bought new boots.
I recommend replacing them all together, reason, by the time you need to have them resoled the shank is probably twisted to some degree which isn't good at all for the foot. I'd put that money into a new pair....