Two things will happen(assuming ideal conditions
1)It will carb naturally in the keg, but it will be hard to tell when it has reached the proper psi (without hooking it up to the regulator)
2)It will eventually level out to serving psi unless you force more C02 or let it come to room temperature again.
I have a similar setup, several kegs with only one gas line. I find it easiest to force carb each keg to what ever psi, then switch the gas line when serving, and when done, top it off to original psi. A little hassle from moving the gas line, but I have great carb kegs all the time.
Primary: Ginger Beer
Kegged: UpstateMike's Caramel Apple Cider, Strawberry Graff
Bottled: Edwort's Apfelwein, Brandon O's Graff, More Graff, Spiced Graff, Ginger Beer
Up Next: Graham's English Cider