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.
An IDE is no substitute for an Intelligent Developer.