Nothing is tied to the specific game disc on either the PS3 or Xbox 360 as far as I'm aware. You didn't specify which system. You could start a game on a Redbox rental for instance, and then continue it on a purchased game. As long as you have the save game data still, it should work.
To answer the question, no. There is no way. The best way would be to just press X (A on XBox) when the game starts loading. If you accidentally load into story mode, you can use the Switcher and choose the bottom character to switch to your online character instead of having to go through the menu.
Best Answer
The stories of GTAV and GTAIV are entirely separate. You can play either without the other and the story will make sense.