ESC's generally have a 3 pin servo style connector, a power connector, and motor leads.
Having said that, the servo connector may be used to connect both a throttle control line from the RX,
and RX operating power from an ESC's internal BEC. The usual current capability is less than 3A max (peak) from the BEC.
The power connector is less standardized, particularly on small models "ready to use" out of the box.
I assume you are trying to use a connector with a pigtail already attached. A 650-750 NMIH pack is not intended to provide high current. They were often used to
power a TX, and usually supplied less than ~100 ma to the TX.
The current should be low enough, although you might notice a small decrease in speed.