in theory yes. there are even high-end brands, delivering battery packs for their streaming solution, but…
It comes with some disadvantages.
- Battery packs will be drawn empty rapidly, as the rPi really likes 2A+
- You can solve this by using a battery-pack that has a feed through (when empty it will forward the charging adapter’s output)
- To avoid issues when the feed through is activated, you need a low noise PSU
- As you already need a low noise PSU, use that PSU and forget the battery pack
