The XSLT action maintains a pool of transformers, depending on how many threads you have configured.
AFAIK, in general each action pipeline instance has one instance per <action .../>, and each ESB-aware listener in an ESB service has one action pipeline instance. So the direct answer to your question is NO.
Tom, please correct me if I'm wrong.
The actions can either be instantiated once per action per pipeline or have a new instance created per invocation, depending on how they have been defined. If the action implements ActionPipelineProcessor or ActionLifecycle, directly or indirectly, or has methods annotated with the Process annotation then there will only be one instance per action per pipeline, otherwise there will be an instance created per invocation.
XsltAction implements ActionPipelineProcessor and ActionLifecycle so has a single instance per action per pipeline.