Answer
ArcIMS 4.0.1
JPEG2000 image files are not supported in ArcIMS 4.0.1 for both the Image Server and ArcMap Server.
ArcIMS 9.0
JPEG2000 image files are not supported in ArcIMS 9.0 using the Image Server.
JPEG2000 image files are supported in ArcIMS 9.0 for the ArcMap Server on Windows and Solaris.
ArcIMS 9.0.1
JPEG2000 image files are not supported in ArcIMS 9.0.1 using the Image Server.
JPEG2000 image files are supported in ArcIMS 9.0.1 for the ArcMap Server on Linux and Solaris.
ArcIMS 9.1
JPEG2000 image files are supported in ArcIMS 9.1 for the ArcMap Server on Linux, Solaris and Windows.
JPEG2000 image files are supported in ArcIMS 9.1 for the Image Server on Solaris and Windows.
ArcIMS 9.2
JPEG2000 image files are supported in ArcIMS 9.2 on Windows and Solaris.
ArcIMS 9.3
JPEG2000 image files are supported in ArcIMS 9.3 on Windows and Solaris.