Would the alternator not being plugged in cause the the engine to start and not stay running.

Like just run for a second and cut off.

 

Bump

 

yes and no.the battery is used to help start the car and the alternator keeps the current flowing . . so if your alt isnt working or working right the car will run off the bat.. so at some point that battery wont be able to keep that car running shut off. check you fuel plugs and make sure you dont have any vac leaks.

 

sounds like you have a different problem.
if the battery was weak, it wouldn't start the car.
now if the car did start, and dies seconds later, you shouldn't be able to start because (assuming) the car ran off the battery.