Yes, it is possible if Hard Disk Sentinel Professional runs as a service: then it can examine hard disk status even if there is no user logged to the computer or if the user does not have administrator rights (have limited rights only).
Generally in order to access the disk status, the software would require administrator user rights, this is why by default Hard Disk Sentinel needs to be run with administrator account.
It is possible to use the software differently: switch to NT Service mode after installation, by using Configuration -> Integration -> Use as service button. It switches Hard Disk Sentinel Professional to "service" mode: then it runs in the context of the SYSTEM account, invisible in the background as an NT service and works independenty from the current user, without any visible user interface.
This way it can work (detect status, issue alerts by e-mail, report problems) independently from the current user and his user rights, so works even if the current user has limited user rights - or if there is no logged user at all. So in service mode, Hard Disk Sentinel Pro is separated from the current user.
When running in service mode, the current user (with limited rights) can start a "Hard Disk Sentinel Tray" extension: with it, the user can get status information and tray icons showing the actual hard disk temperature, but without the opportunity to change options, configuration or perform tests etc. The idea is to let administrator use all functions/features - and if there is an user with limited user rights, he can still check status, but should have no rights to perform any special actions.
Please check https://www.hdsentinel.com/help/en/330_c_integration.html for more details about the service mode in general.