This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
I wouldn't recommend it. You can get into all sorts of trouble - the servlets may someday end up in separate VMs, so it would be physically impossible. Even if not, this is a dangerous way to organize things, as you're creating non-obvious dependencies both on data and on thread processes. It would be safer if you could extract the common functionality into a component in its own right. For simple cases, this might just be a library class. If there's more complexity or shared data, I'd recommend looking at Enterprise JavaBeans.
Customer surveys are for companies who didn't pay proper attention to begin with.