While the battery you linked would be capable of powering two T200 thrusters and a Thruster Commander, at full throttle it would only last around (1300 mAh)/(2 * 22000 mA per thruster)*(60 min/hour) = 2 minutes. For comparison, the batteries we sell on our shop have 18 Ah capacities, meaning they will last over ten times as long.
Also the Thruster Commander comes with a power cable for XT90 connectors (as opposed to the XT60 on the battery you linked), so you would need a different power cable to power the Thruster Commander with that battery.
The power supply has overload protection and should work fine! Won’t damage the thrusters as long as you choose one with an appropriate output voltage between 12-18v.