what happens if you do not suicide in limbo? will you wake up once the sedative wears off?

Take saitos case as an example. What if Cobb suicided with fischer and
Ariadne and saito was left alone in limbo? Wouldn't saito wake up
after the sedative has worn off? So why did Cobb bother to look for
him in limbo?

PS just watched the movie and am a little confused.