I think it will charge your phone. It will just do it slowly.
the s3 can probably do **UPTO** 1.3 A rate. This would just be a slower 0.5 amp charge.
So this is a 0.5a*4=2.0a charger (2 amps is the rate)... it will charge your 2100mah (capacity) battery. (kinda like how you can charge your phone off laptop usb power, but it will just do it slowly)
Yeah, I realize it'll charge my phone but it'll take FOREVER! I'd rather spend more and get a power bank with a bigger capacity (10,000mah-12,000mah) and with more comparable specs to my phone.