The Image Server Extension in ArcGIS for Server 10.1 gets authorized when you authorize the core ArcGIS for Server product (i.e., it's just another ECP number that gets put in when running the registration wizard). I am thinking that it is not limited to a single machine especially if you have an Enterprise License Agreement (ELA). In any event, the extension will need to be authorized on any server from which you wish to host/publish image services. So, technically speaking you could install and authorize it across your site's various servers if you planned to publish at least one image service on each. However, it may be true that all servers in the site require authorization from a technical standpoint if any of their SOCs are to be used to run any image services. If that's the case (and you should ask Esri), then cluster off one server within the site to run the image services. Best course of action is to ask Esri about their rules on this topic from a licensing standpoint and about whether or not each server in the site is required to have it if clustering is not used.
