Answer
No, the ESRI products, ArcGIS Server, ArcEngine, ArcIMS, and ArcSDE, require a new ECP registration code for each released product version. For example, an ECP file specifically created for 9.2 is needed to authorize the 9.2 software, and a 9.3 ECP file is needed to authorize the 9.3 software version.
See the links in the Related Information section below for ESRI Customer Service information on product registration, such as obtaining a new registration number or an authorization file.