You have misinterpreted the meaning of the supported environment pages. Esri never specifies a "maximum OS". All it does is report tested and certified configurations. Older configurations are unsupported, and for newer ones, the Supported Environment Policy states:
That environment is supported if it meets or exceeds the base build environment and that environment is known to not fail.
Your risk is in using an ancient operating system, with an ancient Oracle install, with ancient Java components, quite likely on ancient hardware. Each of these things is individually much more hazardous to your infrastructure than using SP2 over SP1 on an OS which already requires additional payment for security patch updates.
You cannot leave your geodatabase at 9.3.1, because 9.3.1 geodatabases are not supported with ArcGIS 10.3 ("connect only to upgrade").
ArcGIS 10.3 already requires an Oracle 11g or 12c client to connect to 10gR2 databases; you should start preparing for the day when Oracle 10gR2 is not supported at all.