The Pi 3 will draw up to about 800 mA. If you attach USB peripherals, each of them may draw an additional 500 mA maximum, as per the USB 2.0 specs. Thus, in theory, it should work.
However, in practice USB chargers may present two issues:
- Voltage may be lower than the 5V indicated on the label. The Pi 3 will show a voltage warning if voltage drops below 4.7–4.8V.
- The charger may not actually be capable of supplying the current indicated on the label.
The cable may also matter, as their resistance may differ. For both voltage and current, this may make the difference between just above and just below the threshold. If you experience such issues with one cable, go for another which is shorter and/or has thicker wires.
None of these are major issues when charging a USB device—it’ll just take a bit longer. The Pi, on the other hand, is pickier. If voltage or current are below its requirements, you may get the power warning on screen, USB peripherals may fail, the Pi might reboot spontaneously or even fail to boot up in the first place.
I’ve just learned this the hard way with two Pi 3s, one of them with an external hard disk connected.
- Charger #1, rated at 1200 mA: The Pi without the hard disk would occasionally show the power warning, while the Pi with the external hard disk would not even boot.
- Charger #2, rated at 1000 mA: Both Pis initially worked fine. However, on the Pi with the external hard disk, the disk would frequently fail under high load.
- Charger #3, a dual-port charger rated at 1000 mA: seems to work, the Pi with the external HD occasionally displayed a power warning but no failures so far, even after several hours of high load (same use case that would very soon cause disk failures with charger #2).
Takeaway: it depends on the charger. There’s an official power supply for the Pi 3, which has been designed specifically for this use case (but may not work as a generic USB charger). USB chargers may or may not work—unfortunately there’s no easy way to tell other than by trying it out.