You can start a new singleplayer game. If you land on Manhattan immediately, you are in Open SP mode. If a cutscene begins, you have no Open SP activated.
Also, you don't even need to have OpenSP activated all the time, except when starting new OpenSP files. I've got tonnes of save files that get me into OpenSP (each with a different ship, so if I want to test a ship again I don't have to go out and buy it again) without having the OpenSP mod activated.
Known as on Discovery RP 24/7: Thomas_Hill - Train [KNF]TakajiKimura - Chimera
You may also know me elsewhere as I'll Begin or something including "Volbeat"