Yes, it is possible. You would run it from the command line, shortcut, or batch file like this:
7thHeaven.exe /PROFILE:Default /LAUNCH
Just change Default to another profile name if you have a different specific one set up that you want to use. 7th Heaven also supports the /QUIT switch, however, it will immediately open, load your profile, launch the game, then exit, so that is kind of pointless because none of your mods would work once it quits. So, you unfortunately would still have the GUI up. I'll consider adding a proper /QUIT command in a future version of 7H.
I would suggest making a batch file or other script look for the FF7.exe process running in some way, then do a taskkill command to 7thHeaven.exe once the FF7 process ends so you wouldn't have to manually close it.