Yes, do unplug, and they keep going.
As stated already several times in this thread, and has been much debate in other Active vs Passive threads, there's a huge misconception of what an "active bass" really is. While EMGs do really have passive pickups - the HZ series - the active EMG pickups does NOT EVER work without any kind of juice, like a 9v battery. If they do, chances are that it is a EMG HZ passive pickup attached to whatever preamp, or eq in it. I e you can change out those HZ pickups to whatever else passive, and the bass will work the same.
EMG active pickups STILL needs at least one 9v battery and can't ever be run without one. If the battery gone dead, so does the pickups.
The general consensus is that EMG active pickups is at a sales ratio of 9/10 compared to their passive ones. And if you happen to have their cheapo passive ones, chances are that if you swap them out to almost any other passive pickup brand, they are better. EMG has taken a lot of flak for their passive design. Compared to their active ones, everything passive just blows out of the water. If you choose EMG you choose them for their active ones. Not passive. If you should choose passive, there are others that are considerably better in all areas. And more priceworthy too.
AFAIK, no one has told me if there's another pickup maker that does totally active pickups, like EMGs. Like in: they won't ever work without batteries. Not even Seymour Duncans livewires.
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Again from EMGs site (the one pdf file linked to above):
"Battery Life: The typical 9-Volt Alkaline battery is rated at 500 maH (Milliamp Hours). Lithium batteries can be rated as high as 1200 maH. The more current capacity (maH) the battery has, the longer it will last. The most important specification (known as the “hours to cutoff voltage”) is often not specified by the makers. The cutoff voltage is typically 1/2 of the original battery voltage, or 4.5V in this case. Because batteries are used in so many different types of applications it’s hard to predict battery life. See: Nine-volt battery - Wikipedia, the free encyclopedia"
AND THE MOST IMPORTANT THING THAT EMG SAYS:
"Battery Death: When the battery is coming to the end of its useful life, and headroom is limited, you will notice a distortion at the initial attack of the string. It will sound like an unnatural (ech!) and you should consider changing the battery. If you just have EMG Pickups in your guitar without any accessories the pickups will operate on a 2.5 Volt battery. Accessories will have a higher threshold, typically about 4.5 Volts. Always, ALWAYS! install a new battery"
Conclusion:
- if you have ONE active EMG pickup, it will still operate flawlessly without any degradation at all, down to 2.5 volt!
- if you have TWO or more accessories installed, they will operate at just above 4.5 volt still, without any audible difference from full 9v.
- It takes a long time before any 9v battery reaches 2.5 volt. Most people scraps them and considers them dead by that reading in any battery checker.
So, the general rule of thumb, is that you don't need to change the 9v battery, until they hit the 4.5 volt level. It takes quite a while for a 9v battery to go down to 4.5 v or even 2.5 v and it will show up as a dead battery whenever put into a battery checker. Anything below "green" or "good" in a battery checker is battery swap. However, EMGs can still run with "showing red" batteries. Take this into account when using lithium batteries then. Little wonder they last 8 years or more.
Mind you, this is just EMG mileage. Not to be mistaken to be used as a guideline for any other active bass, or active ciremg or any cuit.