Yes. If you're powering the camera from an external source via the USB-C cable, you can remove the internal battery and run the camera via external power. The camera will continue to work normally.
An advantage of leaving the internal battery in place is as a safety net in case the external power stops flowing. Without the internal battery, the moment that the AC power stops, the camera will turn off. It won't turn back on automatically when the power source is restored. With the internal battery installed, it will switch over seamlessly. But there are times where removing the battery might be a better option, especially for very long-term shooting such as timelapse.
External Power Indicator
Usually, when you connect external power you'll get the charging battery indicator. Without any internal battery to charge, though, there's a different icon on the front screen. It looks like this:
Common GoPro Questions
Here are some common questions I get from GoPro users.
Is it normal for GoPro cameras to get hot?
Yes. Depending on the model and the shooting mode you're using, it's normal for GoPros to get quite warm while shooting. They can get hot enough to be uncomfortable to touch. It's especially noticeable when shooting high-resolution and high-framerate video. Some newer models have an overheating protection mechanism that will shut the camera down if it gets too hot. I have more details on GoPros getting hot, here.
How can I control a GoPro remotely?
GoPro makes a range of wireless remote controls. They don't all work with all GoPros--for example, the HERO (2018) isn't compatible with this type of remote control. Many of the newer models also work with the GoPro mobile app. Not every model can be controlled remotely, but most of the newer models have wireless compatibility that can be used for at least some methods of remote control.
Can you take pictures with a GoPro?
If you've been using a GoPro for a while, this might seem pretty obvious, but if you've never used one, it's not quite so self-evident. GoPros are best known for dramatic action videos, but they can most certainly take still photos too. In fact, they can be a very interesting alternative to a traditional camera so long as you work within its limitations. I have more more details here.
Do GoPro wireless controls work underwater?
No. You can't use the mobile app or a wireless remote control if the camera is fully submerged in water. They will normally work just fine in rain and spray--just not submerged. I have a more detailed explanation here.
Do GoPro touchscreens work underwater?
No. If they're just wet above water, they can work to some extent, although often less reliably. But the touchscreens won't work underwater.