Yes, you can charge your phone whilst live streaming via micro USB connected to a power source.
Please be aware that successful charging is dependent on phones age and battery condition, we suggest doing the following to preserve battery and lengthen your live streams.
1. Turn down the brightness on your phone to around 60-70%.
2. Close down all background apps.
3. Purchase a faster charging cable. A faster charger cable has larger internal wires (mostly 24 gauge) that can carry larger currents of 2A or more.