Is it ok to use my MacBook 2009 without battery? Does it harm MacBook using without battery?

There is a followup question in that page that asks how much performance drops when run without the battery. Apple has seen fit to let the link provided die but I remember the actual figure from when it was active. Running without the battery reduces clock speed to one-half the processor's rated speed or 1ghz, whichever is greater.

In a desktop computer, large capacitors are used to stabilize the DC power supplies to the computer so that surges and dips do not propagate into the power for the electronics.

In a Notebook computer, optimized for light weight, those capacitors are not present. Instead, the innate capacity of the battery to maintain a fixed Voltage and reduce surges in current is used as the buffer to keep surges and sags out of the power supplied to the electronics.

It is considered an acceptable risk to bench test a computer without a battery while working on it.

For reliable day-to-day use, a battery -- even a horrible old one -- is required to smooth the power inputs to the computer. Not using a battery in day-to-day use exposes the delicate electronics to the perils of unstable power, with no buffer.

Running a Macbook Pro without the battery - Forums - CNET