This is no matter regarding the OS, about what options a shell script supports. There are also scripts on Linux that do not have a status option. It has nothing to do with AIX or Linux.
If the script does not support a status option and you don't want to do a ps (I don't see any problem in this), you can only hope it is being handled by the AIX System Resource Controller (SRC), which I doubt in that case. You can check the status of supported Subsystems, Subsystem Groups and Subsyserver of it with lssrc -a and grep for it's name, for example.
Though, I assume this software you are controlling by this script is not part of the SRC at all.
Anyway here is a documentation from IBM about SRC, if you are interessted:
IBM Info Center - System Resource Controller
Another option might be to implement a status option into the script by yourself - though on updates it might be overwritten.