NBU Appliances monitored with Solarwinds

If the version / component of Solarwinds you are using requires the installation of a monitoring agent then i doubt that would be supported.

You could reach out to your Symantec Partner or better still raise a support case to get a definitive answer but i doubt that Symantec will let you install anything on an appliance

If there is no agent then the appliance just runs SUSE Linux and NetBackup so it should be able to do what ever it would do with a normal SUSE server

You can setup SNMP traps for hardware and software errors of the appliances.  This can be done very easily from the web interface.  

Setting >> SNMP Server 

It even has a MIB file to help you figure out which traps are worth watching.  Solar winds should easily work with these. 

Sully