Since the OP didn't elaborate, the entire purpose of the smog pump is to pump O2 into either the heads during warmup (to feed the pre cats) or the lower cats during normal use. The O2 is used in the cat converters to help "convert" some of the harmful gases. These are how older 3-way cats work. They need O2 as part of the process, and the air pump, which is what it really does, supplies fresh O2 to them.
Modern 2-way cats don't depend on o2 as part of the process, so this is why air pumps aren't on newer cars. Simply not needed.
So, the air pump can be removed if: You are not running ay cats, or you changed to modern 2-way cats which some aftermarket vendors now sell.
If you still run stock 3-way style cats, and need to pass a sniffer, you NEED the air pump running. If you no longer need to pass a sniffer, and remove it, the cats won't be as effective. You may notice a bigger stench when standing behind the car.
smog pump stuff is like 5-10 pounds, and 0.25HP