If the battery is removed from a MacBook or MacBook Pro, the computer will automatically reduce the processor speed. This prevents the computer from shutting down if it demands more power than the A/C adaptor alone can provide.
Apple support article HT2332%

And that’s a good thing, do stay with me, while I talk about battery remove-ness.

In my experience, people will run laptops without batteries for three reasons:

1. Trying to preserve the life of their battery.
2. They have a battery which doesn’t hold a charge, aka a dead battery.
3. Battery + laptop don’t fit into the docking station.

Trying to preserve battery life.
Batteries degrade every time you charge & discharge.  It’s a fact.  So, people remove the battery when they have mains power available.  I wouldn’t do this.  My three-year old T43 ThinkPad never had it’s battery removed, and it’s battery coped just fine.

The battery is dead, Jim.
Sometimes a battery will just up and die on you.  Given OEM replacement batteries are hilariously expensive*, people cope without them.  Gone are the bad old days of Compaq laptops which refused to power up when there was no “good” battery present.

Battery + laptop don’t fit into the docking station
My ThinkPad, with the extended life battery, couldn’t be used with a port replicator.  The battery stuck out the back of the laptop too far.  The solution was to remove the battery AND curse IBM whenever the mains power failed.  Or upgrade to the full docking station, with the large power supply.

On the MacBook support article …
The Apple engineer who thought of doing this, is a genius.  To know your subject so well to say “What would happen if a user uses a MacBook without a battery”.

% I’m getting old.  Apple technical information documents used to be called TIDs.

* one popular laptop vendor wanted $300 dollars for a replacement.  If I order an extra battery when buying a new (same model) laptop, the “extra” battery only costs $100.  Go figure.