Can MacBooks run without a battery?
It is well-known that any MacBook with battery removed will run at significantly lower clock speed, typically around 1 GHz. The reason is that the power supply is good enough to supply plenty of power for the average usage, but not for bursts. If your hard drive spins up while the CD drive spins up while all cores and the GPU work full blast and you are charging two iPhones then the power supply won't have enough power for that, but it can take extra power from the battery. 

With no battery, the MacBook will turn its power consumption down so that it can guarantee to always have enough power, because otherwise you would have instant crashes at the wrong times.

Another reason to not remove the battery is that dust will have a chance to get deeper inside your MacBook that would otherwise be blocked by the battery. So unless your battery is swollen, leave it in, even if it only has ten minutes charge left.