Say I have a portable power bank with two USB ports providing 2a each. If I connect both the ports to the same device using a Y cable would I therefore have an output of 4a?
As you said if want to charge somthing at 4A(thats a lot of current). If you want to charge mobile at 4A by Y connector then its not possible. You smarphone's battery limit current to 1A/2A to charge it safely. If it charge at 2A max then nothing happend if you use connect Y connecter with both USB ports. It always limit current to 2A.
Also for smartphone only quick chargers can handle that much currentbut it also have inbuilt circuit and kernel to handle that power.
It is advisable to use stock chargers to charge smartphones or other device to charge it quickest.